This post discusses the solutions to the problems from IIT JAM Mathematical Statistics (MS) 2021 Question Paper - Set B. You can find solutions in video or written form.
Note: This post is getting updated. Stay tuned for solutions, videos, and more.
A sample of size is drawn randomly (without replacement) from an urn couraining
balls, of which
are red balls and
are black balls. Let
denote the number of red balls in the selected sample. If
and
then which of the following statements is/are TR UE?
Options -
Answer: ;
Let be a random sample from a distribution with probability density function
where is unknown.
If , then which of the following statements is/are TRUE?
Options -
1. is the unique uniformly minimum variance unbiased estimator of
2. is the unique uniformly minimum variance unbiased estimator of
3. is the unique uniformly minimum variance unbiased estimator of
Answer: is the unique uniformly minimum variance unbiased estimator of
is the MLE of
Consider the linear system , where
is an
matrix,
is an
vector of unknowns
and is an
vector. Further, suppose there exists an
vector
such that the linear system
has No solution. Then, which of the following statements is/are necessarily TRUE?
Options -
1.If and
is the first column of
, then the linear system
has a unique solution
2.If then the linear system
has a solution other than
.
Answer:
Let be independent and identically distributed random variables with probability density function
Then, which of the following random variables has/have finite expectation?
Options -
Answer: ,
,
Let be a random sample from
where
is unknown. Consider the problem of testing
against
Let
denote the power function of the likelihood ratio test of size
for testing
against
. Then. which of the following statements is/are TRUE?
Options -
1.The critical region of the likelihood test of size is
Answer: for all
Let be a random sample from a distribution with probability density function
where is unknown. If
and
then which
of the following statements is/are TRUE?
Options -
1. is a complete and sufficient statistic for
Answer: is a complete and sufficient statistic for
is jointly sufficient for
Distribution of does NOT depend on
Let be a random sample from a distribution with probability density function
where is unknown. Then, which of the following statements is/are TRUE?
Options -
1 .There does NOT exist any unbiased estimator of which attains the Cramer-Rao lower bound
2.Cramer-Rao lower bound, based on for the estimand
is
3 .Cramer-Rao lower bound. based on for the estimand
is
4 .There exists an unbiased estimator of which attains the Cramer-Rao lower bound
Answer:
Cramer-Rao lower bound. based on for the estimand
is
There exists an unbiased estimator of which attains the Cramer-Rao lower bound
Let be a twice differentiable function. Then, which of the following statements is/are necessarily TRUE?
Options-
Answer:
If then
has a solution in (0,1)
is bounded on [8,10]
Let be a
real matrix such that
and the sum of the entries in each row of
is
. Then which of the following statements is/are necessarily TRUE?
Options -
Answer:
The characteristic polynomial, of
has
as a factor
Consider the function
If , then which of the following statements is/are TRUE?
Options -
Answer:
The maximum value of on
is
The minimum value of on
is
This post discusses the solutions to the problems from IIT JAM Mathematical Statistics (MS) 2021 Question Paper - Set B. You can find solutions in video or written form.
Note: This post is getting updated. Stay tuned for solutions, videos, and more.
A sample of size is drawn randomly (without replacement) from an urn couraining
balls, of which
are red balls and
are black balls. Let
denote the number of red balls in the selected sample. If
and
then which of the following statements is/are TR UE?
Options -
Answer: ;
Let be a random sample from a distribution with probability density function
where is unknown.
If , then which of the following statements is/are TRUE?
Options -
1. is the unique uniformly minimum variance unbiased estimator of
2. is the unique uniformly minimum variance unbiased estimator of
3. is the unique uniformly minimum variance unbiased estimator of
Answer: is the unique uniformly minimum variance unbiased estimator of
is the MLE of
Consider the linear system , where
is an
matrix,
is an
vector of unknowns
and is an
vector. Further, suppose there exists an
vector
such that the linear system
has No solution. Then, which of the following statements is/are necessarily TRUE?
Options -
1.If and
is the first column of
, then the linear system
has a unique solution
2.If then the linear system
has a solution other than
.
Answer:
Let be independent and identically distributed random variables with probability density function
Then, which of the following random variables has/have finite expectation?
Options -
Answer: ,
,
Let be a random sample from
where
is unknown. Consider the problem of testing
against
Let
denote the power function of the likelihood ratio test of size
for testing
against
. Then. which of the following statements is/are TRUE?
Options -
1.The critical region of the likelihood test of size is
Answer: for all
Let be a random sample from a distribution with probability density function
where is unknown. If
and
then which
of the following statements is/are TRUE?
Options -
1. is a complete and sufficient statistic for
Answer: is a complete and sufficient statistic for
is jointly sufficient for
Distribution of does NOT depend on
Let be a random sample from a distribution with probability density function
where is unknown. Then, which of the following statements is/are TRUE?
Options -
1 .There does NOT exist any unbiased estimator of which attains the Cramer-Rao lower bound
2.Cramer-Rao lower bound, based on for the estimand
is
3 .Cramer-Rao lower bound. based on for the estimand
is
4 .There exists an unbiased estimator of which attains the Cramer-Rao lower bound
Answer:
Cramer-Rao lower bound. based on for the estimand
is
There exists an unbiased estimator of which attains the Cramer-Rao lower bound
Let be a twice differentiable function. Then, which of the following statements is/are necessarily TRUE?
Options-
Answer:
If then
has a solution in (0,1)
is bounded on [8,10]
Let be a
real matrix such that
and the sum of the entries in each row of
is
. Then which of the following statements is/are necessarily TRUE?
Options -
Answer:
The characteristic polynomial, of
has
as a factor
Consider the function
If , then which of the following statements is/are TRUE?
Options -
Answer:
The maximum value of on
is
The minimum value of on
is