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Mathematical Statistics - 2015 Past Year Paper - IIT JAM MCQ


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30 Questions MCQ Test - Mathematical Statistics - 2015 Past Year Paper

Mathematical Statistics - 2015 Past Year Paper for IIT JAM 2024 is part of IIT JAM preparation. The Mathematical Statistics - 2015 Past Year Paper questions and answers have been prepared according to the IIT JAM exam syllabus.The Mathematical Statistics - 2015 Past Year Paper MCQs are made for IIT JAM 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Mathematical Statistics - 2015 Past Year Paper below.
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Mathematical Statistics - 2015 Past Year Paper - Question 1

Let X1,..., Xn be a random sample from a population with probability density function

where θ > 0 is an unknown parameter.

Then, the uniformly minimum variance unbiased estimator for 

Mathematical Statistics - 2015 Past Year Paper - Question 2

Let X1,...,X100 be independent and identically distributed N(0, 1) random variables. The correlation between 

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Mathematical Statistics - 2015 Past Year Paper - Question 3

Consider the problem of testing H0 :  θ = 0 against H1 : θ = 1/2 based on a single observation X from U(θ, θ + 1) population. The power of the test 

Mathematical Statistics - 2015 Past Year Paper - Question 4

The probability mass function of a random variable X is given by

where k is a constant. The moment generating function MX(t) is

Mathematical Statistics - 2015 Past Year Paper - Question 5

Suppose A and B are events with P(A) = 0.5, P(B) = 0.4 and = 0.2. Then P(Bc | A È B) is equal to

Mathematical Statistics - 2015 Past Year Paper - Question 6

Let X1,..., Xn be a random sample from a Gamma(α, β) population, where β > 0 is a known constant. The rejection region of the most powerful test for H0 : α = 1 against H1 : α = 2 is of the form

Mathematical Statistics - 2015 Past Year Paper - Question 7

Which of the following is NOT a linear transformation?

Mathematical Statistics - 2015 Past Year Paper - Question 8

If a sequence {xn} is monotone and bounded, then

Mathematical Statistics - 2015 Past Year Paper - Question 9

be defined by f(x) = x(x – 1)(x – 2). Then

Mathematical Statistics - 2015 Past Year Paper - Question 10

Which of the following statements is true for all real numbers x ?

Mathematical Statistics - 2015 Past Year Paper - Question 11

Let X1 ,..., Xn be a random sample from a Poisson (θ) population, where q > 0 is unknown. The Cramer- Rao lower bound for the variance of any unbiased estimator of g(θ) = θe equals

Mathematical Statistics - 2015 Past Year Paper - Question 12

Let X and Y be two independent random variables such that X ~ U(0, 2) and Y ~ U(1, 3).Then P(X < Y) equals

Mathematical Statistics - 2015 Past Year Paper - Question 13

There are two boxes, each containing two components. Each component is defective with probability 1/4, independent of all other components. The probability that exactly one box contains exactly one defective component equals

Mathematical Statistics - 2015 Past Year Paper - Question 14

Consider a normal population with unknown mean m and variance σ2 = 9. To test H0 : μ = 0 against H1 : μ ≠ 0, a random sample of size 100 is taken. Based on this sample, the test of the form  rejects the null hypothesis at 5% level of significance. Then, which of the following is a possible 95%confidence interval for μ ?

Mathematical Statistics - 2015 Past Year Paper - Question 15

Let X1 ,..., Xn be a random sample from a population with probability density function

where q > 0 is unknown. The maximum likelihood estimator of θ is

Mathematical Statistics - 2015 Past Year Paper - Question 16

Let X1,..., Xn be a random sample from a population with probability density function

where θ > 0 is unknown. Then, a consistent estimator for θ is

Mathematical Statistics - 2015 Past Year Paper - Question 17

Let the probability density function of a random variable X be given by

Mathematical Statistics - 2015 Past Year Paper - Question 18

Let X be a single observation from a population having an exponential distribution with mean 1/λ. Consider the problem of testing H0 : λ = 2 against H1 : λ = 4. For the test with rejection region X > 3, let α = P(Type I error) and β = P(Type II error). Then

Mathematical Statistics - 2015 Past Year Paper - Question 19

Let Y be an exponential random variable with mean 1/θ, where q > 0. The conditional distribution of X given Y has Poisson distribution with mean Y. Then, the variance of X is

Mathematical Statistics - 2015 Past Year Paper - Question 20

2000 cashew nuts are mixed thoroughly in flour. The entire mixture is divided into 1000 equal parts and each part is used to make one biscuit. Assume that no cashews are broken in the process. A biscuit is picked at random. The probability that it contains no cashew nuts is

Mathematical Statistics - 2015 Past Year Paper - Question 21

Suppose X1,...,Xn are independent random variables and Xk ~ N(0, kσ2), k = 1, ..., n, where σ2 is unknown. The maximum likelihood estimator for σ2 is

Mathematical Statistics - 2015 Past Year Paper - Question 22

Let X1 ,..., X10 be independent and identically distributed U(–5, 5) random variables. Then, the distribution of the random variable

Mathematical Statistics - 2015 Past Year Paper - Question 23

be a differentiable function so that f(x) f’(x) < 0 for all x. Then, which of the following is necessarily true?

Mathematical Statistics - 2015 Past Year Paper - Question 24

Let M be the matrix  Which of the following matrix equations does M satisfy?

Mathematical Statistics - 2015 Past Year Paper - Question 25

If the determinant of an n × n matrix A is zero, then

Mathematical Statistics - 2015 Past Year Paper - Question 26

Then, the number of roots of f is

Mathematical Statistics - 2015 Past Year Paper - Question 27

The number of distinct real values of x for which the matrix 

is singular is

Mathematical Statistics - 2015 Past Year Paper - Question 28

 is a continuous function.

Then h’(1) is equal to

Mathematical Statistics - 2015 Past Year Paper - Question 29

Let A be a 5 × 3 real matrix of rank 2. be a non- zero vector that is in the column space of A. Let S =  Define the translation of a subspace V of  as the set x0 + V = {x0 + v : v ∈ V}. Then

Mathematical Statistics - 2015 Past Year Paper - Question 30

 a differentiable function whose derivative is continuous. Then

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