Probability-Probability Distributions (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 103 - 106 of 109

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Question number: 103

» Probability » Probability Distributions » Joint and Marginal Distributions

MCQ▾

Question

Continuous random variables X and Y have a joint distribution with density function f(x,y)=x2+xy3 for 0<x<1 and 0<y<2 . Find P[X>12 Y>12].

Choices

Choice (4) Response

a.

1316

b.

4364

c.

4352

d.

Question does not provide sufficient data or is vague

Question number: 104

» Probability » Probability Distributions » Gamma

MCQ▾

Question

A chi-square (with n degree of freedom) probability density function satisfies which of the following property/properties?

Choices

Choice (4) Response

a.

If n=2 then f is decreasing with f(0)=1

b.

If 0<n2 , then f is concave downward.

c.

If 0<n<2 , f is increasing with f(x) as x0 .

d.

All a. , b. and c. are correct

Question number: 105

» Probability » Probability Distributions » Beta

MCQ▾

Question

If X has the F distribution with n>0 degrees of freedom in the numerator and d>0 degrees of freedom in the denominator then, Y=(nd)X1+(nd)X will follow ________ distribution.

Choices

Choice (4) Response

a.

N(0,nd)

b.

Chisquare with n degrees of freedom.

c.

Beta(n2,d2)

d.

Question does not provide sufficient data or is vague

Question number: 106

» Probability » Probability Distributions » Distributions of Functions of Random Variables

MCQ▾

Question

Suppose X1 and X2 are independent exponential random variables with parameter λ=1 . If Y1=X1X2,Y2=X1+X2 . Then the marginal distribution of Y1 or Y2 will follow ________.

Choices

Choice (4) Response

a.

Exponential distribution with parameter λ=2

b.

Poisson distribution with parameter λ=2

c.

Exponential distribution with parameter λ=1

d.

None of the above

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