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Mathematical Statistics - 2016 Past Year Paper - IIT JAM MCQ


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30 Questions MCQ Test - Mathematical Statistics - 2016 Past Year Paper

Mathematical Statistics - 2016 Past Year Paper for IIT JAM 2024 is part of IIT JAM preparation. The Mathematical Statistics - 2016 Past Year Paper questions and answers have been prepared according to the IIT JAM exam syllabus.The Mathematical Statistics - 2016 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 - 2016 Past Year Paper below.
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Mathematical Statistics - 2016 Past Year Paper - Question 1

Let 

Then rank of P equals 

Mathematical Statistics - 2016 Past Year Paper - Question 2

Let α , β,γ be real numbers such that β ≠ 0 and γ ≠ 0. Suppose

and P-1 =P.  Then    

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Mathematical Statistics - 2016 Past Year Paper - Question 3

Let m > 1. The volume of the solid generated by revolving the region between the y-axis and the curve xy = 4, 1 < y < m, about the y-axis is 15π. The value of m is   

Mathematical Statistics - 2016 Past Year Paper - Question 4

Consider the region S enclosed by the surface z = y2  and the planes z = 1,x = 0, x = 1, y = -1 and y = 1. The volume of S is  

Mathematical Statistics - 2016 Past Year Paper - Question 5

Let X be a discrete random variable with the moment generating function 

Then P (X < 1) equals 

Mathematical Statistics - 2016 Past Year Paper - Question 6

Let E and F be two independent events with 

Then P(E) equals 

Mathematical Statistics - 2016 Past Year Paper - Question 7

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

Then E (X2)

Mathematical Statistics - 2016 Past Year Paper - Question 8

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

Then the distribution of the random variable Y = loge X-2a is 

Mathematical Statistics - 2016 Past Year Paper - Question 9

Let X1 ,X2 ,.....  be a sequence of i.i.d. N (0,1) random variables.  converges in probability to  

Mathematical Statistics - 2016 Past Year Paper - Question 10

Consider the simple linear regression model with n random observations Yi = β0+ β1xi + εi, i = 1,....,n, (n > 2). β0  and β1 are unknown parameters, x1,....,xn are observed values of the regressor variable and ε1... ,εn are error random variables with E (εi) = 0, i = 1,....,n, and for i, j = 1,...., n,   For real constants is an 
unbiased estimator of β1 , then

Mathematical Statistics - 2016 Past Year Paper - Question 11

Let (X, Y) have the joint probability density function 

Then P(Y <1 | X = 3) equals 

Mathematical Statistics - 2016 Past Year Paper - Question 12

Let X1,X2,..... be a sequence of  i.i.d. random variables having the probability density function 

If the distribution of converges to N ( 0,1) as 
n → ∞, then a possible value of α is 

Mathematical Statistics - 2016 Past Year Paper - Question 13

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

If Tn = min {X1,...,Xn}, then

Mathematical Statistics - 2016 Past Year Paper - Question 14

Let X1,...,Xn be i.i.d. random variables with the probability density function 

If X(n) = max {X1,...,Xn},   

Mathematical Statistics - 2016 Past Year Paper - Question 15

Let X and Y be two independent N ( 0,1) random variables. Then P (0 < X2 + Y2 < 4) equals 

Mathematical Statistics - 2016 Past Year Paper - Question 16

Let X be a random variable with the cumulative distribution function 

Then E (X) equals 

Mathematical Statistics - 2016 Past Year Paper - Question 17

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

For a suitable constant K, the critical region of the most powerful test for testing H0 : θ =1 against H1 : θ = 2 is of the form 

Mathematical Statistics - 2016 Past Year Paper - Question 18

Let X1,...,Xn, Xn+1, Xn+2,..., Xn+m (n > 4,m > 4) be a random sample from N (μ ,σ2);

 then the distribution of the random variable 

  

is

Mathematical Statistics - 2016 Past Year Paper - Question 19

Let X1,...,Xn (n > 1) be a random sample from a Poisson (θ) population, θ > 0, and Then  the uniformly minimum variance unbiased estimator of θ2 is   

Mathematical Statistics - 2016 Past Year Paper - Question 20

Let X be a random variable whose probability mass functions f(x | H0) (under the null hypothesis H0)  and f (x |H1) (under the alternative hypothesis H1)  are given by 

For testing the null hypothesis H0 : X~f (x | H0)  against the alternative hypothesis H1 : X~f (x | H1),  consider the test given by: Reject

If α = size of the test and β = power of the test, then 

Mathematical Statistics - 2016 Past Year Paper - Question 21

Let X1,..,Xn be a random sample from a N (2θ, θ2) population, θ > 0. A consistent estimator for θ is

Mathematical Statistics - 2016 Past Year Paper - Question 22

An institute purchases laptops from either vendor V1  or vendor V2 with equal probability. The lifetimes (in years) of laptops from vendor  V1  have a U (0, 4) distribution, and the lifetimes (in years) of laptops from vendor V2 have an Exp (12) distribution.  If a randomly selected laptop in the institute has lifetime more than two years, then the probability that it was supplied by vendor V2 is  

Mathematical Statistics - 2016 Past Year Paper - Question 23

Let y (x)  be the solution to the differential equation 

Mathematical Statistics - 2016 Past Year Paper - Question 24

Let an = e -2n sin n and bn = e-n n2 (sin n)2 for n >1. Then

Mathematical Statistics - 2016 Past Year Paper - Question 25

Let 

Then 

Mathematical Statistics - 2016 Past Year Paper - Question 26

 be a twice differentiable function. Further, let f (0) = 1, f(2) = 2  and f(4) = 3.   Then

Mathematical Statistics - 2016 Past Year Paper - Question 27

Let f (x,y) = x2 - 400 x y2 for all (x,y)  Then f attains its 

Mathematical Statistics - 2016 Past Year Paper - Question 28

Let y (x) be the solution to the differential equation  

Then y (1) equals   

Mathematical Statistics - 2016 Past Year Paper - Question 29

The area between the curve y = g" (x) and the x-axis over the interval [0, 2] is 

Mathematical Statistics - 2016 Past Year Paper - Question 30

singular matrix such that for a nonzero vectorand

Then

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