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## IGNOU PGDAST Post Graduate Diploma in Applied Statistics (Specialisation in Industrial Statistics)

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GET SOLVED ASSIGNMENTS

EMAIL : [email protected]

WEBSITE : MBASOLVEDASSIGNMENT.COM

CALL US: 9773820734 (Whatsapp)

IGNOU PGDAST Post Graduate Diploma in Applied Statistics (Specialisation in Industrial Statistics)

DEHRADUN

DELHI-1

DELHI-2

DELHI-3

GUWAHATI

HYDERABAD

JABALPUR

JAIPUR

JAMMU

JORHAT

KARNAL

KHANNA

KOHIMA

KOLKATA

KORAPUT

LUCKNOW

MADURAI

MUMBAI

NAGPUR

NOIDA

PANAJI

PATNA

PORT BLAIR

PUNE

RAGHUNATHGANJ

RAIPUR

RAJKOT

RANCHI

SHILLONG

SHIMLA

SILIGURI

SRINAGAR

TRIVANDRUM

VARANASI

VIJAYAWADA

Booklet-I

ASSIGNMENT BOOKLET

Post Graduate Diploma in Applied Statistics

(Specialisation in Industrial Statistics)

MST-001 to MSTL-002

(Valid from 1st January, 2019 to 31st December, 2019)

School of Sciences

Indira Gandhi National Open University

Maidan Garhi, New Delhi-110068

It is compulsory to submit the assignments

before filling the Examination Form.

Dear Student,

Please read the information on assignments in the Programme Guide that we have sent you after

your enrolment. A weightage of 30%, as you are aware, has been earmarked for continuous

evaluation, which would consist of one tutor-marked assignment for this course. The

assignments for MST-001 to MSTL-002 have been given in this booklet.

Instructions for Formatting Your Assignments

Before attempting the assignment, please read the following instructions carefully:

1) On top of the first page of your answer sheet, please write the details exactly in the following

format:

ENROLLMENT NO :……………………………………………

NAME :……………………………………………

ADDRESS :……………………………………………

……………………………………………

……………………………………………

PROGRAMME CODE: ………………………..

COURSE CODE: ……………………………….

COURSE TITLE: ………………………………

STUDY CENTRE: ………………………..……. DATE: ……………….………………...

PLEASE FOLLOW THE ABOVE FORMAT STRICTLY TO FACILITATE

EVALUATION AND TO AVOID DELAY.

2) Use only foolscap size writing paper (but not of very thin variety) for writing your answers.

3) Leave 4 cm margin on the left, top and bottom of your answer sheet.

4) Your answers should be precise.

5) This assignment is to be submitted at the Study Centre.

We strongly suggest that you should retain a copy of your answer sheets.

6) This assignment is valid up to December 31, 2019.

7) You cannot fill the Exam Form for this course till you have submitted this assignment. So

solve it and submit it to your study centre at the earliest. If you wish to appear in the

TEE, June 2019, you should submit your TMAs by March 31, 2019. Similarly, If you wish

to appear in the TEE, December 2019, you should submit your TMAs by September 30,

2019.

We wish you good luck.

TUTOR MARKED ASSIGNMENT

MST-001: Foundation in Mathematics and Statistics

Course Code: MST-001

Assignment Code: MST-001/TMA/2019

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1. State whether the following statements are True or False. Give reason in support of your

answer: (5×2=10)

(a)The nth term of the sequence 1 , 1 , 1, 2, ... is 1 ( 2)n .

4 2 4

− − −

(b)Symmetric difference of two sets A = {1, 2, 3} and B = {2, 3, 7, 9} is {1, 3, 7}.

(c)

x 5

x 5

lim 1

→ x 5

−

=

−

(d) Ratio scale is highest level of measurement scale because here measurements of the

characteristic under study can be positive or negative or both.

(e)The range of the data shown in the following frequency distribution is 350:

Classes 0-50 50-100 100-150 150-200 200-250 250-300 300-350

Frequencies 10 20 30 40 30 20 0

2 (a) In a city having total population of 1,00,000, out of which 10,000 can read and speak

English, 88000 can read and speak Hindi and 80000 can read and speak Hindi only. Find

how many of them can read and speak:

(i) Both the languages.

(ii) English only.

(iii) Neither Hindi nor English. (2+1+2)

(b) Show that the set {1, − 2, 4, −8, 16, −32, ...}

is enumerable. (3)

(c) How many 5 digits numbers are possible using 8 digits 2 to 9 such that three digits 2, 5

and 9 are always included? (2)

3. (a) Expand (8 −3x)1/3 by binomial theorem.

(b) Expand (2 − ax)5 by binomial theorem for any index. (5+5)

4. Discuss the continuity and differentiability of the following function at x = 9.

x 9, x 9

f (x)

0, x 9

⎧⎪ − ≠ = ⎨

= ⎪⎩

(5+5)

5. Evaluate the following integrals:

i) 2

3x dx

(x + 2)(x −1) ∫

ii)

9

2

f (x) dx

f (x) + f (11− x) ∫ (6+4)

6. (a) Without expanding prove that

4 5 1

4 8 8 0

7 3 19

− − =

(b) Draw box plot for batting scores of the player given below: (5+5)

Player 10, 62, 22, 8, 90, 13, 105, 155, 25, 53, 6, 4, 52, 57, 27

7. (a) Find a matrix B such that

1 3 2 1 3 2 1 0 0

B 1 4 5 1 4 5B 0 1 0

2 5 6 2 5 6 0 0 1

− − = − − =

(10)

(b) A researcher visits 100 families and collects the information. He/she has ten questions in

his/her questionnaire listed below from i to x. Assume that he/she gets information from

all 100 families for all the 10 questions. He/she arranges this information in a data frame

having 100 rows (each corresponding to response of a family) and 10 columns (each

corresponding to a question in his questionnaire). To analyse this data first he/she has to

find out scale (nominal, ordinal, interval or ratio) of each column. If he/she is your friend

then write scale of each of 10 variables in his/her data frame.

i) Number of members in the family

ii) Age of the oldest person of the family

iii) Sex of the oldest person of the family

iv) Highest education qualification among the family members of the family

v) Monthly income of the family

vi) Saving (Income in that particular month − expenditure in the same month) of the

family. Keep in mind that expenditure may be more that income in that particular

month of some family(ies)

vii) Number of mobile phones in the family

viii) Height of tallest person of the family

ix) Does the family have landline telephone?

x) Monthly mobile bill of the family (10×1=10)

8. The following table shows the life (in weeks) of a sample of 15-watt LED bulbs produced by a

manufacturer:

Life Time of LED

50 33 47 73 15

11 98 24 72 37

19 82 07 53 51

36 61 02 25 34

21 42 45 08 15

32 23 26 06 17

15 44 53 55 41

71 77 74 28 13

18 13 55 81 06

05 35 85 17 53

52 03 60 64 42

14 58 04 21 32

91 21 21 09 17

35 11 72 12 18

32 20 14 76 11

13 15 34 23 32

i) Form a frequency distribution by taking suitable width,

ii) Form cumulative frequency curves (ogives) on one

graph.

iii) Find the average (median) of the life of LED bulbs with

the help of ogives.

(5+12+3)

TUTOR MARKED ASSIGNMENT

MST-002: Descriptive Statistics

Course Code: MST-002

Assignment Code: MST-002/TMA/2019

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1. State whether the following statements are true or false and also give the reason in support of

your answer: (5×2=10)

a) If the regression coefficients bYX and bXY of a data are 1.6 and 0.4, respectively, then the

value of r(X, Y) is 0.8.

b) If each value of X is multiplied by 10 and each value of Y is multiplied by 20, then the

modified regression coefficient bXY would be the half of previous one.

c) If (AB) = 10, (αB) = 15, (Aβ) = 20 and (αβ) = 30 then A and B are associated.

d) If standard deviation of x is 5, standard deviation of y = 2x–3 is 7.

e) If with usual notations for two attributes the inequality (AB) (αβ) < (αB) (Aβ) holds, then

−1 ≤ Q ≤ 1.

2. a) Find the missing information from the following data:

Group I Group II Group III Combined

Number 50 ? 90 200

Standard Deviation 6 7 ? 7.746

Mean 113 ? 115 116

b) If AM and GM of two numbers are 30 and 18, respectively, find the numbers. (7+3)

3. a) For the following distribution, calculate first four central moments using recurrence

relations:

Marks: 2.7-7.5 7.5-12.5 12.5-17.5 17.5-22.5 22.5-27.5 27.5-32.5 32.5-37.5

Frequency: 06 13 23 39 19 15 05

Also find the coefficients of skewness and kurtosis. (8)

b) Calculate the first, second and third quartile for the following data:

Class: 0-10 10-20 20-30 30-40 40-50

Frequency: 05 15 30 12 08

Also find the quartile deviation and coefficient of quartile deviation. (6)

5 a) A researcher collects the following information for two variables x and y:

n = 20, r = 0.5, mean (x) = 15, mean (y) = 20, σx = 4 and σy = 5

Later it was found that one pair of values (x, y) has been wrongly taken as (16, 30)

whereas the correct values were (26, 35). Find the correct value of r(x, y). (10)

b) Calculate the coefficient of rank correlation for the following data:

X: 48 33 40 09 16 16 65 24 16 57

Y: 13 13 24 06 15 04 20 09 06 19

(07)

6 a) Explain the method of least squares. Fit a straight line Y = a +b X to the following data:

X: 1 3 5 7 9 10

Y: 5 8 12 15 18 22 (5)

b) The equations of two regression lines are given as follows:

5x – 15y = 30

10x−20y = 15

Calculate (i) regression coefficients, byx and bxy; (ii) correlation coefficient r(x, y);

(iii) Mean of X and Y; and (iv) Value of σy if σx = 3. (10)

7. (a) In a trivariate distribution:

4, 6, r 0.5, r r 0.8 1 2 3 12 23 31 σ = σ = σ = = = =

Find (i) 23.1 r , (ii) R , 1.23 (iii) b ,b and 12.3 13.2 (iv) 1.23 σ (10)

ii. Suppose a computer has found for a given set of values of X1, X2 and X3: r12=0.90, r13=0.30

and r23=0.70. Examine whether these computations are error free. (4)

8 a) A company is interested in determining the strength of association between the

communication time of their employees and the level of stress-related problems observed

on job. A study of 120 assembly line workers reveals the following data:

Stress

High Moderate Low Total

Under 20 min. 10 10 15 35

20-50 min 15 10 25 50

Over 50 min 15 10 10 35

Total 40 30 50 120

Determine the amount of association between the communication time of their employees

and the level of stress using coefficient of contingency and interpret the result. (12)

b) 600 candidates were appeared in an examination. The boys outnumbered girls by 15% of

all candidates. Number of passed exceeded the number of failed candidates by 300. Boys

failing in the examination numbered 80. Determine the coefficient of association. (8)

TUTOR MARKED ASSIGNMENT

MST-003: Probability Theory

Course Code: MST-003

Assignment Code: MST-003/TMA/2019

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1. State whether the following statements are True or False and also give the reason in

support of your answer. (5×2=10)

(a) If A and B are any two events defined on a sample space S then P(A∪B) = P(S) always

holds.

(b) Cumulative distribution function of a discrete random variable is always strictly

increasing.

(c) If X is a discrete random variable with probability mass function (pmf)

X 0 1 2 3

P[X = x] 1

8

1

4

1

2

a

then value of a will be 1.

(d) If X and Y are two independent random variables then P[X ≥ 2|Y > 1] < P[X ≥ 2].

(e) Suppose that you spin the dial shown in the figure so that it comes to rest at a random

position.

The probability that the dial will land somewhere between 0 and 45 will be 1/4.

2. First check whether the following function is a valid density function? If it is a valid

density then obtain its cumulative probability function F(x). If it is a valid density then finally

calculate P(7 ≤ X ≤ 8) either using f(x) or F(x).

2 (x 5), 5 X 10

f (x) 25

0, otherwise

⎧ − ≤ ≤ = ⎪⎨⎪⎩

if x < 0 (3+3+4)

3. (a) The joint density function of random variables X and Y is given by

14e 2x 7y , x 0, y 0

f (x,y)

0, otherwise

⎧ − − ≥ ≥ = ⎪⎨⎪⎩

Are X and Y independent? (6)

(b) A particular game is played where the contestant spins a wheel that can land on the

number 1, 5, 30 with probabilities of 0.50, 0.45 and 0.05, respectively. The contestant

pays INR5 to play the game and is awarded the amount of money indicated by the

number where the spinner lands. Is this a fair game? [By fair, it is meant that the

contestant should have an expected return equal to the price she pays to play the game.]

(4)

4. (a) Suppose two fair dice are tossed where each of the 36 possible outcomes is equally likely

to occur. Knowing that the first die shows a 4, what is the probability that the sum of the

two dice equals at least 7. (5)

(b) Suppose that there are m students in a room. What is the probability that at least two of

them have the same birthday? Assume that every day of the year is equally likely to be a

birthday, and disregard leap years. That is, assume there are always 365 days to a year.

[Hint: Attack the problem by first calculating probability of complement event and then

use P(E) = 1 – P( E)] (5)

5. The A taxi cab company has 12 Ambassadors and 8 Fiats. If 5 of these taxi cabs are in the

workshop for repair and an Ambassador is as likely to be in for repair as a Fiat, what is

the probability that (i) 3 of them are Ambassadors and 2 are Fiats, (ii) at least 3 of them

are Ambassadors, and (iii) all 5 are of the same make? (2+4+4)

6. (a) The probability that a player hits a target is 0.24. He fires 6 times. What is the probability

of hitting the target exactly twice? (5)

(b) What is the probability that 5th success is obtained in 9th trail if probability of success and

failure do not vary from trial to trail. (5)

7. (a) Metro trains in a certain city run every 9 minutes between 6.15 a.m. to 11.15 p.m. What

is the probability that a commuter entering the station at a random time during this period

will have to wait at least five minutes? (5)

(b) Obtain mean and variance for the beta distribution whose density is given by

3

9

f (x) 280x , 0 x

(1 x)

= < < ∞

+

(5)

8. (a) A car manufacturer purchases car batteries from two different suppliers A and B.

Suppose supplier A provides 60% of the batteries and supplier B provides the rest. If 6%

of all batteries from supplier A are defective and 4% of the batteries from supplier B are

defective. Determine the probability that a randomly selected battery is not defective.

(b) An item is produced by a machine in large numbers. The machine is known to produce

5% defectives. A quality control engineer is testing the items randomly. What is the

probability that at least 5 items are examined in order to get 2 defectives? (10+10)

TUTOR MARKED ASSIGNMENT

MST-004: Statistical Inference

Course Code: MST-004

Assignment Code: MST-004/TMA/2019

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1. State whether the following statements are True or False. Give reason in support of your

answer: (5×2=10)

(a) If the probability density function of a random variable X follows t-distribution is

, x 0

(1 x )

f (x) 1 2 ≥

π +

=

then degrees of freedom of the distribution will be 2.

(b) The cars that enter in a Metro parking are classified either Indian-made or Foreign-made.

To check that the car ender in the parking is in random order, we use Mann Whitney U

test.

(c) A random variable has the pdf

≤ ≤ θ

θ

f (x) = 1 , 0 x

If the critical region of testing the null and alternative hypothesesH : 2 0 θ = and

H : 2 0 θ ≠ is X >1then type-I error will be 0.5.

(d) If sample mean (X) is consistent estimator of the parameter θthen log(X) also consistent

for log(θ).

(e) In a random sample of 525 families owning television set in the region of New Delhi, it is

found that 370 subscribe to Star Plus. A 99% confidence interval for the actual proportion

of such families in New Delhi which subscribe to Star Plus will be (0.66, 0.74).

2. A baby-sister has 6 children under her supervision. The age of each child is as follows:

i) Find the mean and SD of this finite population.

ii) List all possible sample of size 3 from this population without replacement.

iii) Construct the sampling distribution of mean.

Child Age(in years)

Sonu 10

Rishi 8

Lavnik 6

Chiya 4

Aman 2

Avishi 6

iv) Compute the mean and standard error of the mean of the sampling distribution obtained

in (iii). (2+3+2+3)

3. (a) A Pizza company would like to determine the average delivery time it can promise its

customers. How large should the sample size be if it wants to be 95% confident that the

sample estimate would not differ from the actual average delivery time by more than 1.5

minutes? The previous studies have shown the SD to be 7 minutes. (4)

(b)A sample of 400 shops was selected in a large metropolitan area to determine various

information concerning to the consumer behaviour. One question, among the questions,

asked, was “Do you enjoy shopping for clothing?” Out of 200 males,170 answered yes.

Out of 250 females, 224 answered yes. Find 95% confidence interval for the difference of

the proportions for enjoys shopping for clothing. (6)

4. The following data relate to the number of items produced in a shift by two workers A and B

for some days:

9

8

14

15

12

13

19

17

16

17

20

21

19

20

Determine whether there is significant difference in terms of (i) doctor’s and (ii)

treatments. (12)

8 a) Generate a complete cycle for the LCG given x (5 x 3) i (i 1) = + − Mod(16), with x 5" 0 = . A

man tosses an unbiased coin 10 times. Using the first 10 random numbers generated

above, obtain a sequence of heads and tails. (10)

b) Following U(0,1) were generated by a random number generation method:

0.251 0.769 0.153 0.575 0.390 0.335 0.066 0.104 0.200

0.019 0.597 0.729 0.012 0.922 0.691 0.817 0.064 0.539

0.419 0.305 0.449 0.998 0.919 0.470 0.372 0.851 0.643

0.509 0.913 0.445 0.464 0.447 0.279 0.413 0.494 0.972

0.983 0.432 0.368 0.574

Apply chi-square test to test the fit the distribution. (10)

TUTOR MARKED ASSIGNMENT

MSTE-001: Industrial Statistics-I

Course Code: MSTE-001

Assignment Code: MSTE-001/TMA/2019

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1. State whether the following statements are True or False. Give reason in support of your

answer: (5×2=10)

GET SOLVED ASSIGNMENTS

EMAIL : [email protected]

WEBSITE : MBASOLVEDASSIGNMENT.COM

CALL US: 9773820734 (Whatsapp)

EMAIL : [email protected]

WEBSITE : MBASOLVEDASSIGNMENT.COM

CALL US: 9773820734 (Whatsapp)

IGNOU PGDAST Post Graduate Diploma in Applied Statistics (Specialisation in Industrial Statistics)

DEHRADUN

DELHI-1

DELHI-2

DELHI-3

GUWAHATI

HYDERABAD

JABALPUR

JAIPUR

JAMMU

JORHAT

KARNAL

KHANNA

KOHIMA

KOLKATA

KORAPUT

LUCKNOW

MADURAI

MUMBAI

NAGPUR

NOIDA

PANAJI

PATNA

PORT BLAIR

PUNE

RAGHUNATHGANJ

RAIPUR

RAJKOT

RANCHI

SHILLONG

SHIMLA

SILIGURI

SRINAGAR

TRIVANDRUM

VARANASI

VIJAYAWADA

Booklet-I

ASSIGNMENT BOOKLET

Post Graduate Diploma in Applied Statistics

(Specialisation in Industrial Statistics)

MST-001 to MSTL-002

(Valid from 1st January, 2019 to 31st December, 2019)

School of Sciences

Indira Gandhi National Open University

Maidan Garhi, New Delhi-110068

It is compulsory to submit the assignments

before filling the Examination Form.

Dear Student,

Please read the information on assignments in the Programme Guide that we have sent you after

your enrolment. A weightage of 30%, as you are aware, has been earmarked for continuous

evaluation, which would consist of one tutor-marked assignment for this course. The

assignments for MST-001 to MSTL-002 have been given in this booklet.

Instructions for Formatting Your Assignments

Before attempting the assignment, please read the following instructions carefully:

1) On top of the first page of your answer sheet, please write the details exactly in the following

format:

ENROLLMENT NO :……………………………………………

NAME :……………………………………………

ADDRESS :……………………………………………

……………………………………………

……………………………………………

PROGRAMME CODE: ………………………..

COURSE CODE: ……………………………….

COURSE TITLE: ………………………………

STUDY CENTRE: ………………………..……. DATE: ……………….………………...

PLEASE FOLLOW THE ABOVE FORMAT STRICTLY TO FACILITATE

EVALUATION AND TO AVOID DELAY.

2) Use only foolscap size writing paper (but not of very thin variety) for writing your answers.

3) Leave 4 cm margin on the left, top and bottom of your answer sheet.

4) Your answers should be precise.

5) This assignment is to be submitted at the Study Centre.

We strongly suggest that you should retain a copy of your answer sheets.

6) This assignment is valid up to December 31, 2019.

7) You cannot fill the Exam Form for this course till you have submitted this assignment. So

solve it and submit it to your study centre at the earliest. If you wish to appear in the

TEE, June 2019, you should submit your TMAs by March 31, 2019. Similarly, If you wish

to appear in the TEE, December 2019, you should submit your TMAs by September 30,

2019.

We wish you good luck.

TUTOR MARKED ASSIGNMENT

MST-001: Foundation in Mathematics and Statistics

Course Code: MST-001

Assignment Code: MST-001/TMA/2019

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1. State whether the following statements are True or False. Give reason in support of your

answer: (5×2=10)

(a)The nth term of the sequence 1 , 1 , 1, 2, ... is 1 ( 2)n .

4 2 4

− − −

(b)Symmetric difference of two sets A = {1, 2, 3} and B = {2, 3, 7, 9} is {1, 3, 7}.

(c)

x 5

x 5

lim 1

→ x 5

−

=

−

(d) Ratio scale is highest level of measurement scale because here measurements of the

characteristic under study can be positive or negative or both.

(e)The range of the data shown in the following frequency distribution is 350:

Classes 0-50 50-100 100-150 150-200 200-250 250-300 300-350

Frequencies 10 20 30 40 30 20 0

2 (a) In a city having total population of 1,00,000, out of which 10,000 can read and speak

English, 88000 can read and speak Hindi and 80000 can read and speak Hindi only. Find

how many of them can read and speak:

(i) Both the languages.

(ii) English only.

(iii) Neither Hindi nor English. (2+1+2)

(b) Show that the set {1, − 2, 4, −8, 16, −32, ...}

is enumerable. (3)

(c) How many 5 digits numbers are possible using 8 digits 2 to 9 such that three digits 2, 5

and 9 are always included? (2)

3. (a) Expand (8 −3x)1/3 by binomial theorem.

(b) Expand (2 − ax)5 by binomial theorem for any index. (5+5)

4. Discuss the continuity and differentiability of the following function at x = 9.

x 9, x 9

f (x)

0, x 9

⎧⎪ − ≠ = ⎨

= ⎪⎩

(5+5)

5. Evaluate the following integrals:

i) 2

3x dx

(x + 2)(x −1) ∫

ii)

9

2

f (x) dx

f (x) + f (11− x) ∫ (6+4)

6. (a) Without expanding prove that

4 5 1

4 8 8 0

7 3 19

− − =

(b) Draw box plot for batting scores of the player given below: (5+5)

Player 10, 62, 22, 8, 90, 13, 105, 155, 25, 53, 6, 4, 52, 57, 27

7. (a) Find a matrix B such that

1 3 2 1 3 2 1 0 0

B 1 4 5 1 4 5B 0 1 0

2 5 6 2 5 6 0 0 1

− − = − − =

(10)

(b) A researcher visits 100 families and collects the information. He/she has ten questions in

his/her questionnaire listed below from i to x. Assume that he/she gets information from

all 100 families for all the 10 questions. He/she arranges this information in a data frame

having 100 rows (each corresponding to response of a family) and 10 columns (each

corresponding to a question in his questionnaire). To analyse this data first he/she has to

find out scale (nominal, ordinal, interval or ratio) of each column. If he/she is your friend

then write scale of each of 10 variables in his/her data frame.

i) Number of members in the family

ii) Age of the oldest person of the family

iii) Sex of the oldest person of the family

iv) Highest education qualification among the family members of the family

v) Monthly income of the family

vi) Saving (Income in that particular month − expenditure in the same month) of the

family. Keep in mind that expenditure may be more that income in that particular

month of some family(ies)

vii) Number of mobile phones in the family

viii) Height of tallest person of the family

ix) Does the family have landline telephone?

x) Monthly mobile bill of the family (10×1=10)

8. The following table shows the life (in weeks) of a sample of 15-watt LED bulbs produced by a

manufacturer:

Life Time of LED

50 33 47 73 15

11 98 24 72 37

19 82 07 53 51

36 61 02 25 34

21 42 45 08 15

32 23 26 06 17

15 44 53 55 41

71 77 74 28 13

18 13 55 81 06

05 35 85 17 53

52 03 60 64 42

14 58 04 21 32

91 21 21 09 17

35 11 72 12 18

32 20 14 76 11

13 15 34 23 32

i) Form a frequency distribution by taking suitable width,

ii) Form cumulative frequency curves (ogives) on one

graph.

iii) Find the average (median) of the life of LED bulbs with

the help of ogives.

(5+12+3)

TUTOR MARKED ASSIGNMENT

MST-002: Descriptive Statistics

Course Code: MST-002

Assignment Code: MST-002/TMA/2019

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1. State whether the following statements are true or false and also give the reason in support of

your answer: (5×2=10)

a) If the regression coefficients bYX and bXY of a data are 1.6 and 0.4, respectively, then the

value of r(X, Y) is 0.8.

b) If each value of X is multiplied by 10 and each value of Y is multiplied by 20, then the

modified regression coefficient bXY would be the half of previous one.

c) If (AB) = 10, (αB) = 15, (Aβ) = 20 and (αβ) = 30 then A and B are associated.

d) If standard deviation of x is 5, standard deviation of y = 2x–3 is 7.

e) If with usual notations for two attributes the inequality (AB) (αβ) < (αB) (Aβ) holds, then

−1 ≤ Q ≤ 1.

2. a) Find the missing information from the following data:

Group I Group II Group III Combined

Number 50 ? 90 200

Standard Deviation 6 7 ? 7.746

Mean 113 ? 115 116

b) If AM and GM of two numbers are 30 and 18, respectively, find the numbers. (7+3)

3. a) For the following distribution, calculate first four central moments using recurrence

relations:

Marks: 2.7-7.5 7.5-12.5 12.5-17.5 17.5-22.5 22.5-27.5 27.5-32.5 32.5-37.5

Frequency: 06 13 23 39 19 15 05

Also find the coefficients of skewness and kurtosis. (8)

b) Calculate the first, second and third quartile for the following data:

Class: 0-10 10-20 20-30 30-40 40-50

Frequency: 05 15 30 12 08

Also find the quartile deviation and coefficient of quartile deviation. (6)

5 a) A researcher collects the following information for two variables x and y:

n = 20, r = 0.5, mean (x) = 15, mean (y) = 20, σx = 4 and σy = 5

Later it was found that one pair of values (x, y) has been wrongly taken as (16, 30)

whereas the correct values were (26, 35). Find the correct value of r(x, y). (10)

b) Calculate the coefficient of rank correlation for the following data:

X: 48 33 40 09 16 16 65 24 16 57

Y: 13 13 24 06 15 04 20 09 06 19

(07)

6 a) Explain the method of least squares. Fit a straight line Y = a +b X to the following data:

X: 1 3 5 7 9 10

Y: 5 8 12 15 18 22 (5)

b) The equations of two regression lines are given as follows:

5x – 15y = 30

10x−20y = 15

Calculate (i) regression coefficients, byx and bxy; (ii) correlation coefficient r(x, y);

(iii) Mean of X and Y; and (iv) Value of σy if σx = 3. (10)

7. (a) In a trivariate distribution:

4, 6, r 0.5, r r 0.8 1 2 3 12 23 31 σ = σ = σ = = = =

Find (i) 23.1 r , (ii) R , 1.23 (iii) b ,b and 12.3 13.2 (iv) 1.23 σ (10)

ii. Suppose a computer has found for a given set of values of X1, X2 and X3: r12=0.90, r13=0.30

and r23=0.70. Examine whether these computations are error free. (4)

8 a) A company is interested in determining the strength of association between the

communication time of their employees and the level of stress-related problems observed

on job. A study of 120 assembly line workers reveals the following data:

Stress

High Moderate Low Total

Under 20 min. 10 10 15 35

20-50 min 15 10 25 50

Over 50 min 15 10 10 35

Total 40 30 50 120

Determine the amount of association between the communication time of their employees

and the level of stress using coefficient of contingency and interpret the result. (12)

b) 600 candidates were appeared in an examination. The boys outnumbered girls by 15% of

all candidates. Number of passed exceeded the number of failed candidates by 300. Boys

failing in the examination numbered 80. Determine the coefficient of association. (8)

TUTOR MARKED ASSIGNMENT

MST-003: Probability Theory

Course Code: MST-003

Assignment Code: MST-003/TMA/2019

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1. State whether the following statements are True or False and also give the reason in

support of your answer. (5×2=10)

(a) If A and B are any two events defined on a sample space S then P(A∪B) = P(S) always

holds.

(b) Cumulative distribution function of a discrete random variable is always strictly

increasing.

(c) If X is a discrete random variable with probability mass function (pmf)

X 0 1 2 3

P[X = x] 1

8

1

4

1

2

a

then value of a will be 1.

(d) If X and Y are two independent random variables then P[X ≥ 2|Y > 1] < P[X ≥ 2].

(e) Suppose that you spin the dial shown in the figure so that it comes to rest at a random

position.

The probability that the dial will land somewhere between 0 and 45 will be 1/4.

2. First check whether the following function is a valid density function? If it is a valid

density then obtain its cumulative probability function F(x). If it is a valid density then finally

calculate P(7 ≤ X ≤ 8) either using f(x) or F(x).

2 (x 5), 5 X 10

f (x) 25

0, otherwise

⎧ − ≤ ≤ = ⎪⎨⎪⎩

if x < 0 (3+3+4)

3. (a) The joint density function of random variables X and Y is given by

14e 2x 7y , x 0, y 0

f (x,y)

0, otherwise

⎧ − − ≥ ≥ = ⎪⎨⎪⎩

Are X and Y independent? (6)

(b) A particular game is played where the contestant spins a wheel that can land on the

number 1, 5, 30 with probabilities of 0.50, 0.45 and 0.05, respectively. The contestant

pays INR5 to play the game and is awarded the amount of money indicated by the

number where the spinner lands. Is this a fair game? [By fair, it is meant that the

contestant should have an expected return equal to the price she pays to play the game.]

(4)

4. (a) Suppose two fair dice are tossed where each of the 36 possible outcomes is equally likely

to occur. Knowing that the first die shows a 4, what is the probability that the sum of the

two dice equals at least 7. (5)

(b) Suppose that there are m students in a room. What is the probability that at least two of

them have the same birthday? Assume that every day of the year is equally likely to be a

birthday, and disregard leap years. That is, assume there are always 365 days to a year.

[Hint: Attack the problem by first calculating probability of complement event and then

use P(E) = 1 – P( E)] (5)

5. The A taxi cab company has 12 Ambassadors and 8 Fiats. If 5 of these taxi cabs are in the

workshop for repair and an Ambassador is as likely to be in for repair as a Fiat, what is

the probability that (i) 3 of them are Ambassadors and 2 are Fiats, (ii) at least 3 of them

are Ambassadors, and (iii) all 5 are of the same make? (2+4+4)

6. (a) The probability that a player hits a target is 0.24. He fires 6 times. What is the probability

of hitting the target exactly twice? (5)

(b) What is the probability that 5th success is obtained in 9th trail if probability of success and

failure do not vary from trial to trail. (5)

7. (a) Metro trains in a certain city run every 9 minutes between 6.15 a.m. to 11.15 p.m. What

is the probability that a commuter entering the station at a random time during this period

will have to wait at least five minutes? (5)

(b) Obtain mean and variance for the beta distribution whose density is given by

3

9

f (x) 280x , 0 x

(1 x)

= < < ∞

+

(5)

8. (a) A car manufacturer purchases car batteries from two different suppliers A and B.

Suppose supplier A provides 60% of the batteries and supplier B provides the rest. If 6%

of all batteries from supplier A are defective and 4% of the batteries from supplier B are

defective. Determine the probability that a randomly selected battery is not defective.

(b) An item is produced by a machine in large numbers. The machine is known to produce

5% defectives. A quality control engineer is testing the items randomly. What is the

probability that at least 5 items are examined in order to get 2 defectives? (10+10)

TUTOR MARKED ASSIGNMENT

MST-004: Statistical Inference

Course Code: MST-004

Assignment Code: MST-004/TMA/2019

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1. State whether the following statements are True or False. Give reason in support of your

answer: (5×2=10)

(a) If the probability density function of a random variable X follows t-distribution is

, x 0

(1 x )

f (x) 1 2 ≥

π +

=

then degrees of freedom of the distribution will be 2.

(b) The cars that enter in a Metro parking are classified either Indian-made or Foreign-made.

To check that the car ender in the parking is in random order, we use Mann Whitney U

test.

(c) A random variable has the pdf

≤ ≤ θ

θ

f (x) = 1 , 0 x

If the critical region of testing the null and alternative hypothesesH : 2 0 θ = and

H : 2 0 θ ≠ is X >1then type-I error will be 0.5.

(d) If sample mean (X) is consistent estimator of the parameter θthen log(X) also consistent

for log(θ).

(e) In a random sample of 525 families owning television set in the region of New Delhi, it is

found that 370 subscribe to Star Plus. A 99% confidence interval for the actual proportion

of such families in New Delhi which subscribe to Star Plus will be (0.66, 0.74).

2. A baby-sister has 6 children under her supervision. The age of each child is as follows:

i) Find the mean and SD of this finite population.

ii) List all possible sample of size 3 from this population without replacement.

iii) Construct the sampling distribution of mean.

Child Age(in years)

Sonu 10

Rishi 8

Lavnik 6

Chiya 4

Aman 2

Avishi 6

iv) Compute the mean and standard error of the mean of the sampling distribution obtained

in (iii). (2+3+2+3)

3. (a) A Pizza company would like to determine the average delivery time it can promise its

customers. How large should the sample size be if it wants to be 95% confident that the

sample estimate would not differ from the actual average delivery time by more than 1.5

minutes? The previous studies have shown the SD to be 7 minutes. (4)

(b)A sample of 400 shops was selected in a large metropolitan area to determine various

information concerning to the consumer behaviour. One question, among the questions,

asked, was “Do you enjoy shopping for clothing?” Out of 200 males,170 answered yes.

Out of 250 females, 224 answered yes. Find 95% confidence interval for the difference of

the proportions for enjoys shopping for clothing. (6)

4. The following data relate to the number of items produced in a shift by two workers A and B

for some days:

9

8

14

15

12

13

19

17

16

17

20

21

19

20

Determine whether there is significant difference in terms of (i) doctor’s and (ii)

treatments. (12)

8 a) Generate a complete cycle for the LCG given x (5 x 3) i (i 1) = + − Mod(16), with x 5" 0 = . A

man tosses an unbiased coin 10 times. Using the first 10 random numbers generated

above, obtain a sequence of heads and tails. (10)

b) Following U(0,1) were generated by a random number generation method:

0.251 0.769 0.153 0.575 0.390 0.335 0.066 0.104 0.200

0.019 0.597 0.729 0.012 0.922 0.691 0.817 0.064 0.539

0.419 0.305 0.449 0.998 0.919 0.470 0.372 0.851 0.643

0.509 0.913 0.445 0.464 0.447 0.279 0.413 0.494 0.972

0.983 0.432 0.368 0.574

Apply chi-square test to test the fit the distribution. (10)

TUTOR MARKED ASSIGNMENT

MSTE-001: Industrial Statistics-I

Course Code: MSTE-001

Assignment Code: MSTE-001/TMA/2019

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1. State whether the following statements are True or False. Give reason in support of your

answer: (5×2=10)

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