Mathematical Statistics - 2016 Past Year Paper

# Mathematical Statistics - 2016 Past Year Paper - IIT JAM

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## 60 Questions MCQ Test IIT JAM Past Year Papers and Model Test Paper (All Branches) - Mathematical Statistics - 2016 Past Year Paper

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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

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 vector and Then

*Multiple options can be correct
Mathematical Statistics - 2016 Past Year Paper - Question 31

For two nonzero real numbers a and b, consider the system of linear equations *Multiple options can be correct
Mathematical Statistics - 2016 Past Year Paper - Question 32 Which of the following statements is (are) TRUE?

*Multiple options can be correct
Mathematical Statistics - 2016 Past Year Paper - Question 33  Which of the following statements is (are) TRUE?

*Multiple options can be correct
Mathematical Statistics - 2016 Past Year Paper - Question 34 Which of the following statements is (are) TRUE?

*Multiple options can be correct
Mathematical Statistics - 2016 Past Year Paper - Question 35

Let E and F be two events with 0 < P (E) < 1, 0 < P (F) < 1  and P (E | F) > P (E).   Which of the following statements is (are) TRUE?

*Multiple options can be correct
Mathematical Statistics - 2016 Past Year Paper - Question 36

Let X1,...,Xn (n > 1) be a random sample from a U (2θ -1, 2θ + 1) population, and Y1 = min {X1,...., Xn} , Yn max {X1,...Xn}. Which of the following statistics is (are) maximum likelihood estimator (s)  of θ ?

*Multiple options can be correct
Mathematical Statistics - 2016 Past Year Paper - Question 37

Let X1,...,Xn be a random sample from a N (0, σ2) population, σ > 0. Which of the following testing problems has (have) the region as the most
powerful critical region of level α ?

*Multiple options can be correct
Mathematical Statistics - 2016 Past Year Paper - Question 38

Let X1,....Xn be a random sample from a N (0, 2θ2) population, θ > 0. Which of the following statements is (are) TRUE?

*Multiple options can be correct
Mathematical Statistics - 2016 Past Year Paper - Question 39

Let X1,...,Xn be a random sample from a population with the probability density function Which of the following is (are) 100 (1 -α) % confidence interval(s) for θ ?

*Multiple options can be correct
Mathematical Statistics - 2016 Past Year Paper - Question 40

The cumulative distribution function of a random variable X is given by Which of the following statements is (are) TRUE?

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 41

Let X1,....,X10 be a random sample from a N (3,12) population. Suppose  distribution, then the value of α is _______________

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 42

Let X be a continuous random variable with the probability density function Then the upper bound of P (X - 2 >1) using Chebyshevs inequality is ________________

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 43

Let X and Y be continuous random variables with the joint probability density function Then P ( X < Y) = _____________________

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 44

Let X and Y be continuous random variables with the joint probability density function Then P (X > 0, Y< 0 ) = _________________________

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 45

Let Y be a Bin random variable.  Using normal approximation to binomial distribution, an approximate value of P ( 22 < Y < 28) is ________________________

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 46

Let X be a Bin (2, p) random variable and Y be a Bin (4, p) random  variable, 0 < p < 1.  If *Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 47

Consider the linear transformation

T(x, y,z) = (2x+ y + z, x+ z, 3x+2 y + z).

The rank of T  is ________________________

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 48 *Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 49 be defined by f (x) = x13 - e-x+ 5 x +6.The minimum value of the function f on [0,13] is__________________________

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 50

Consider a differentiable function f on [ 0,1] with the derivative The arc length of the curve is ________________________

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 51

Let m be a real number such that m > 1. If then m = ______________________

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 52

Let The product of the eigen values of P-1 is ________________________

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 53

The value of the real number m in the following equation is ________________________

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 54  converges to ______________________

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 55

Let X1,X2,...  be a sequence of  i.i.d. random variables with the probability density function  *Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 56

Let X and Y be continuous random variables with the joint probability density function where c is a suitable constant. Then E (X ) = ________________________

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 57

Two points are chosen at random on a line segment of length 9 cm.  The probability that the distance between these two points is less than 3 cm is ______________________

*Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 58

Let X be a continuous random variable with the probability density function  *Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 59

If X is a U ( 0,1) random variable, then *Answer can only contain numeric values
Mathematical Statistics - 2016 Past Year Paper - Question 60

In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________

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