jam.iitm.ac.in Mathematical Statistics Question Paper Sample : Indian Institute of Technology Madras

Name of the Organisation : Indian Institute of Technology Madras
Name of the Exam : JAM Exam
Document Type : Sample Question Paper
Name of the Subject : Mathematical Statistics (MS)

Website : jam.iitm.ac.in
Download Sample Question Paper 2015 : https://www.pdfquestion.in/uploads/7712-MSQP2015.pdf
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Download Sample Question Paper 2013 :  https://www.pdfquestion.in/uploads/7712-MSQP2013.pdf

JAM 2015 Mathematical Statistics Sample Question :

Q.1 Let X1,… Xn be a random sample from a population with probability density function where ? ? 0 is an unknown parameter.Then, the uniformly minimum variance unbiased estimator for 1

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Q.2 Let 1 100 X ,?, X be independent and identically distributed N ?0,1? random variables. The correlation between
(A) 0 (B) 96 98 (C) 98 100 (D) 1
Q.3 Consider the problem of testing 0H against 1H – 0+1, 1 2 based on a single observation X from U 0,0+1,0 population. The power of the test 0 “Reject if 2 ”
(A) 1/6 (B) 5/6 (C) 1/3 (D) 2/3
Q.4 The probability mass function of a random variable X is given by where k is a constant. The moment generating function (t) X M is
Q.5 Suppose A and B are events with P? A? ? 0.5, P?B? ? 0.4 and P? A?Bc ? ? 0.2. Then
(A) 1/2 (B) 1/3 (C) 1/4 (D) 0
Q.7 Which of the following is NOT a linear transformation?
A) T :R3 : R?2 defined by T (x, y, z) ? (x, z)
(B) T :R3 : R3 defined by T (x, y, z) ? (x, y -1, z)
(C) T :R2 : R2 defined by T (x, y) ? (2x, y – x)
(D) T :R2 : R2 defined by T (x, y) ? ( y, x)
Q.8 If a sequence (xn) is monotone and bounded, then
(A) there exists a subsequence of (xn) that diverges
(B) there may exist a subsequence of (xn) that is not monotone
(C) all subsequences of (xn)converge to the same limit
(D) there exist at least two subsequences of (xn) which converge to distinct limits
Let f :R be defined by f (x) ? x(x – 1)(x – 2). Then
(A) f is one-one and onto
(B) f is neither one-one nor onto
(C) f is one-one but not onto
(D) f is not one-one but onto
Q.10 Which of the following statements is true for all real numbers x ?

JAM 2014 Mathematical Statistics :
(A) exactly one root in the interval (1 , 2)
(B) exactly two distinct roots in the interval (1, 2)
(C) exactly three distinct roots in the interval (1, 2)
(D) NO roots in the interval (1 , 2)
A circle of random radius R (in cm) is constructed, where the random variable R has U [0,1] distribution. The probability that the area of the circle is less than 1 cm2, is
Let the random variable X have moment generating function MX(t)=e2′(l+’), te R Then P(X s 2) is
A system consisting of n components functions if, and only if, at least one of ncomponents functions. Suppose that all the 11 components of the system function independently, each with probability 3. If the probability of functioning of the system is g , then the value of n is
(A) 2 (B) 4 (C) 3 (D)
The matrix
1 2 3
M = 0 4 5
O 0 6
(A) is an elementary matrix
(B) can be written as a product of elementary matrices
(C) does NOT have linearly independent eigenvectors
(D) is a nilpotent matrix
Let the mappings 1], T2, T3, 7; from IR3 to R3 be de?ned by
Then which of these are linear transformations of R3 over R?
A) T1 and T2 (B) T2 and T3
(C) T2 and 7;, (D) T3 and T4
Let X1, X 2, X 3 and X 4 be independent random variables. Then which of the following pairs of random variables are independent?
(A) (X1+X2’X2+X3) (B) (Xv X1+X3) (C) (XI‘LXP X3) (D) (X2, X1+X2+X3)
Let X be a random variable of continuous type with probability density function
Based on single observation X , the most powerful test of size a=0.1, for testing H0 :0=1 against H1 :0 = 2, rejects H0 if X < k. Then the value of k is 10 11
(A) 1 (B) — (C) ~3— 3 (D) 4
Let X be a random variable of continuous type with probability density ?lnction f (x). Then, based on single observation X, the most POWCI?ll test of size a=0.1 for testing
Let X and Y be two random variables of discrete type with respective probability mass functions as
Then, among statistics X and Y,
(A) bothX and Y are complete
(B) X is complete but Y is NOT complete
(C) both X and Y are NOT complete
(D) X is NOT complete but Y is complete
Let X and Y denote the lifetimes (in years) of two independent components connected in a series with respective probability density functions
Then the probability that the system will survive for at least 2 years, is
(A) e_2 3e—2 (B) 26—2 (C) (D) 4e_2

JAM 2013 Mathematical Statistics :
Let E and F be two events with P(E)=0.7,P(F)=OAandP(EnF’)=OA. Then p(FIEuF’) is equal to
(A) 1/2 (B)1/3 (C)1/4 (D)1/5
Let f: [O,=)~[O,=) be a twice differentiable and increasing function with f(O) =O. Suppose that, for any t~O,the length of the arc of the curve y=f(x), x~O between
Let A be a 3×3 real matrix with eigenvalues 1,2,3 and let B =K ‘ +A’. Then the trace of the matrix B is equal to
Let XpX” …be a sequence of i.i.d. random variables with variance 1. Then
Let XpX” …,X”,X,,+I be a random sample from a N(Il,I) population.
A) T is unbiased and consistent (C) T is unbiased and inconsistent
(B) T is biased and consistent (D) T is biased and inconsistent
Let X be an observation from a population with density
A continuous random variable Xhas the density
(x) =2 rp(x) <I>(x), XEJR.
Then (A) E(X»O
(C) P(X 5::0»0.5
(B)E(X)<O (D) P(X :2:0)<0.25