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Explore the Back-StoryThis 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.

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 ______________________

**Answer:**

Let,

Then, is equal to _________

**Answer:** 10

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

is ___________________________________

**Answer:**

Let . Then, the value of the integral

is _______

**Answer:** 2

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

**Answer:** 2500

Let be a random variable with moment generating function

Then, is equal to _______

**Answer:** 2

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 ________

**Answer:** 3

Let be a random variable having the probability density function

Then, is equal to _____

**Answer:** 147

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

**Answer:**

Let . Let be the value of the integral

Then, is equal to _______

**Answer:**

Let,

Then, is equal to ____

**Answer:** 3

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 ____

**Answer:** 218

The number of real roots of the polynomial

is ____

**Answer:**

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 ___

**Answer:** 42

Let . Then, is equal to ____

**Answer:** 6

Let and let the joint probability density function

of be

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

**Answer: **1

Let be defined by

If then is equal to ____

**Answer:** 21

Let .

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

**Answer:** 8

Let the random vector have the joint probability mass function

.

Let If and then is equal to ____**Answer:** 225

Let and be independent random variables. Define

Let and . If the correlation coefficient between and is ,

then is equal to ____

**Answer:** 2

- IIT JAM MS (Set B) 2021 Question Paper - Problems and Solutions
- IIT JAM MS (Set A) 2021 Question Paper - Problems and Solutions
- How to Prepare for IIT JAM Statistics?
- Know about the learning Paths
- Our Statistics Program

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.

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 ______________________

**Answer:**

Let,

Then, is equal to _________

**Answer:** 10

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

is ___________________________________

**Answer:**

Let . Then, the value of the integral

is _______

**Answer:** 2

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

**Answer:** 2500

Let be a random variable with moment generating function

Then, is equal to _______

**Answer:** 2

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 ________

**Answer:** 3

Let be a random variable having the probability density function

Then, is equal to _____

**Answer:** 147

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

**Answer:**

Let . Let be the value of the integral

Then, is equal to _______

**Answer:**

Let,

Then, is equal to ____

**Answer:** 3

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 ____

**Answer:** 218

The number of real roots of the polynomial

is ____

**Answer:**

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 ___

**Answer:** 42

Let . Then, is equal to ____

**Answer:** 6

Let and let the joint probability density function

of be

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

**Answer: **1

Let be defined by

If then is equal to ____

**Answer:** 21

Let .

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

**Answer:** 8

Let the random vector have the joint probability mass function

.

Let If and then is equal to ____**Answer:** 225

Let and be independent random variables. Define

Let and . If the correlation coefficient between and is ,

then is equal to ____

**Answer:** 2

- IIT JAM MS (Set B) 2021 Question Paper - Problems and Solutions
- IIT JAM MS (Set A) 2021 Question Paper - Problems and Solutions
- How to Prepare for IIT JAM Statistics?
- Know about the learning Paths
- Our Statistics Program

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