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Mathematical Statistics - 2017 Past Year Paper - IIT JAM MCQ


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30 Questions MCQ Test - Mathematical Statistics - 2017 Past Year Paper

Mathematical Statistics - 2017 Past Year Paper for IIT JAM 2024 is part of IIT JAM preparation. The Mathematical Statistics - 2017 Past Year Paper questions and answers have been prepared according to the IIT JAM exam syllabus.The Mathematical Statistics - 2017 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 - 2017 Past Year Paper below.
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Mathematical Statistics - 2017 Past Year Paper - Question 1

The imaginary parts of the eigenvalues of the matrix

are

Mathematical Statistics - 2017 Past Year Paper - Question 2

Let be such that u = (1 2 3 5)T and v = (5 3 2 1)T. Then the equation uvT x = v has

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Mathematical Statistics - 2017 Past Year Paper - Question 3

Which of the following statements is TRUE ?

Mathematical Statistics - 2017 Past Year Paper - Question 4

 be a sequence defined as follows :

Which of the following statements is TRUE ?  

Mathematical Statistics - 2017 Past Year Paper - Question 5

Let X be a continuous random variable with the probability density function 

Mathematical Statistics - 2017 Past Year Paper - Question 6

Let X be a random variable with the moment generating function

Then P(X > 1) equals

Mathematical Statistics - 2017 Past Year Paper - Question 7

Let X be a discrete random variable with the probability mass function

p(x) = k(1 + |x|)2, x = –2, –1, 0, 1, 2,

where k is a real constant. Then P(X = 0) equals

Mathematical Statistics - 2017 Past Year Paper - Question 8

Let the random variable X have uniform distribution on the interval . Then P(cos X > sin X) is

Mathematical Statistics - 2017 Past Year Paper - Question 9

be a sequence of i.i.d. random variables having common probability density function

Mathematical Statistics - 2017 Past Year Paper - Question 10

Let X1, X2, X3 be a random sample from a distribution with the probability density function

Which of the following estimators of θ has the smallest variance for all θ > 0 ?

Mathematical Statistics - 2017 Past Year Paper - Question 11

Player P1 tosses 4 fair coins and player P2 tosses a fair die independently of P1. The probability that the number of heads observed is more than the number on the upper face of the die, equals

Mathematical Statistics - 2017 Past Year Paper - Question 12

Let X1 and X2 be i.i.d. continuous random variables with the probability density function

Using Chebyshev’s inequality, the lower bound of

Mathematical Statistics - 2017 Past Year Paper - Question 13

Let X1, X2, X3 be i.i.d. discrete random variables with the probability mass function

Let Y = X1 + X2 + X3. Then P(Y > 5) equals

Mathematical Statistics - 2017 Past Year Paper - Question 14

Let X and Y be continuous random variables with the joint probability density function

where c is a positive real constant. Then E(X) equals

Mathematical Statistics - 2017 Past Year Paper - Question 15

Let X and Y be continuous random variables with the joint probability density function

Mathematical Statistics - 2017 Past Year Paper - Question 16

Let X1, X2, ..., Xm, Y1, Y2, ..., Yn be i.i.d. N(0, 1) random variables. Then

has

Mathematical Statistics - 2017 Past Year Paper - Question 17

 be a sequence of i.i.d. random variables with the probability mass function

 then possible values of m and M are

Mathematical Statistics - 2017 Past Year Paper - Question 18

Let x1 = 1.1, x2 = 0.5, x3 = 1.4, x4 = 1.2 be the observed values of a random sample of size four from a distribution with the probability density function

Then the maximum likelihood estimate of θ2 is

Mathematical Statistics - 2017 Past Year Paper - Question 19

 be the observed values of a random sample of size four from a distribution with the probability density function

Then the method of moments estimate of θ is

Mathematical Statistics - 2017 Past Year Paper - Question 20

Let X1, X2 be a random sample from an N(0, θ) distribution, where θ > 0. Then the value of k, for which the interval is a 95% confidence interval for θ, equals

Mathematical Statistics - 2017 Past Year Paper - Question 21

Let X1, X2, X3, X4 be a random sample from N(θ1, σ2) distribution and Y1, Y2, Y3, Y4 be a random sample from N(θ1, σ2) distribution, where θ1, θ2 ∈ (-∞, ∞) and σ > 0. Further suppose that the two random samples are independent. For testing the null hypothesis H0 : θ1 = θ2 against the alternative hypothesis H1 : θ1 > θ2, suppose that a test rejects H0 if and only if   The power of the tes

Mathematical Statistics - 2017 Past Year Paper - Question 22

Let X be a random variable having a probability density function f ∈ {f0, f1}, where

For testing the null hypothesis against  based on a single observation on X, the power of the most powerful test of size α = 0.05 equals

Mathematical Statistics - 2017 Past Year Paper - Question 23

are

Mathematical Statistics - 2017 Past Year Paper - Question 24

Mathematical Statistics - 2017 Past Year Paper - Question 25

Consider the function

f(x, y) = x3 – y3 – 3x2 + 3y2 + 7, x,

Then the local minimum (m) and the local maximum (M) of f are given by

Mathematical Statistics - 2017 Past Year Paper - Question 26

 let the sequence be defined by

Then the values of c for which the seriesconverges are

Mathematical Statistics - 2017 Past Year Paper - Question 27

If for a suitable α > 0,

exists and is equal to

Mathematical Statistics - 2017 Past Year Paper - Question 28

Let

Which of the following statements is TRUE ?

Mathematical Statistics - 2017 Past Year Paper - Question 29

Let Q, A, B be matrices of order n × n with real entries such that Q is orthogonal and A is invertible. Then the eigenvalues of QT A–1 BQ are always the same as those of

Mathematical Statistics - 2017 Past Year Paper - Question 30

be the curve defined by

 

Let L be the length of the arc of this curve from the origin to the point P on the curve at which the tangent is perpendicular to the x- axis. Then L equals

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