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
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