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# IIT JAM MS 2021 Question Paper | Set C | Problems & Solutions

This post discusses the solutions to the problems from IIT JAM Mathematical Statistics (MS) 2021 Question Paper - Set C. You can find solutions in video or written form.

Note: This post is getting updated. Stay tuned for solutions, videos, and more.

## IIT JAM Mathematical Statistics (MS) 2021 Problems & Solutions (Set C)

### Problem 1

Let and be the probability mass functions given by

Consider the problem of testing the mull hypothesis a gainst based on a single
sample If and , respectively, denote the size and power of the test with critical region
then is equal to ______________________

### Problem 2

Let,

Then, is equal to _________

#### Problem 3

Let and be the eigenvalues of If and then the value of
is ___________________________________

### Problem 4

Let . Then, the value of the integral

is _______

### Problem 5

Let be a matrix. If then the value of is ________

### Problem 6

Let be a random variable with moment generating function

Then, is equal to _______

### Problem 7

Let be an observed random sample of size 5 from a distribution with probability density function

is unknown. Then, the maximum likelihood estimate of based on the observed sample is equal to ________

### Problem 8

Let be a random variable having the probability density function

Then, is equal to _____

### Problem 9

Let denote the length of the curve from to . Then, the value of is equal to _____

### Problem 10

Let . Let be the value of the integral

Then, is equal to _______

### Problem 11

Let,

Then, is equal to ____

### Problem 12

Let and be four independent events such that and Let be the probability that at most two events among and occur. Then, is equal to ____

### Problem 13

The number of real roots of the polynomial

is ____

### Problem 14

Let be the region bounded by the parallelogram with vertices at the points (1,0),(3,2) ,
(3,5) and Then. the value of the integral is equal to ___

### Problem 15

Let . Then, is equal to ____

### Problem 16

Let and let the joint probability density function
of be

Then, the covariance between the random variables and is equal to ____

### Problem 17

Let be defined by

If then is equal to ____

### Problem 18

Let .
If is the area of , then the value of is equal to ____

### Problem 19

Let the random vector have the joint probability mass function

.

Let If and then is equal to ____

### Problem 20

Let and be independent random variables. Define

Let and . If the correlation coefficient between and is ,
then is equal to ____

This post discusses the solutions to the problems from IIT JAM Mathematical Statistics (MS) 2021 Question Paper - Set C. You can find solutions in video or written form.

Note: This post is getting updated. Stay tuned for solutions, videos, and more.

## IIT JAM Mathematical Statistics (MS) 2021 Problems & Solutions (Set C)

### Problem 1

Let and be the probability mass functions given by

Consider the problem of testing the mull hypothesis a gainst based on a single
sample If and , respectively, denote the size and power of the test with critical region
then is equal to ______________________

### Problem 2

Let,

Then, is equal to _________

#### Problem 3

Let and be the eigenvalues of If and then the value of
is ___________________________________

### Problem 4

Let . Then, the value of the integral

is _______

### Problem 5

Let be a matrix. If then the value of is ________

### Problem 6

Let be a random variable with moment generating function

Then, is equal to _______

### Problem 7

Let be an observed random sample of size 5 from a distribution with probability density function

is unknown. Then, the maximum likelihood estimate of based on the observed sample is equal to ________

### Problem 8

Let be a random variable having the probability density function

Then, is equal to _____

### Problem 9

Let denote the length of the curve from to . Then, the value of is equal to _____

### Problem 10

Let . Let be the value of the integral

Then, is equal to _______

### Problem 11

Let,

Then, is equal to ____

### Problem 12

Let and be four independent events such that and Let be the probability that at most two events among and occur. Then, is equal to ____

### Problem 13

The number of real roots of the polynomial

is ____

### Problem 14

Let be the region bounded by the parallelogram with vertices at the points (1,0),(3,2) ,
(3,5) and Then. the value of the integral is equal to ___

### Problem 15

Let . Then, is equal to ____

### Problem 16

Let and let the joint probability density function
of be

Then, the covariance between the random variables and is equal to ____

### Problem 17

Let be defined by

If then is equal to ____

### Problem 18

Let .
If is the area of , then the value of is equal to ____

### Problem 19

Let the random vector have the joint probability mass function

.

Let If and then is equal to ____

### Problem 20

Let and be independent random variables. Define

Let and . If the correlation coefficient between and is ,
then is equal to ____

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