ISS Statistics Paper I (New 2016 MCQ Pattern): Questions 316 - 318 of 404

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Question number: 316

» Probability » Probability Distributions » Beta

MCQ▾

Question

For a standard Beta distribution having pdf f(x) , with parameter α(0,)andβ(0,)andα+β2 , which of the following statements is/are correct?

Choices

Choice (4) Response
a.

If α1and0<β<1,f is increasing with f(x)asx1.

b.

If α=1andβ>1,f is decreasing with mode at x=0.

c.

If α>1andβ=1,f is increasing with mode at x=1.

d. All a. , b. and c. are correct

Question number: 317

» Probability » Probability Distributions » Conditional Distributions

MCQ▾

Question

Suppose that the joint density of X and Y is

f(x,y)=125x(2xy)for0<x<1and0<y<1

and zero otherwise. Which of the following is equal to fX Y(x y)fory(0, 1).

Choices

Choice (4) Response
a.

6x(2xy)43y

b.

x(2x+y)43y

c.

3x(2x)26x

d.

3x(2+xy)52y

Question number: 318

» Probability » Probability Distributions » Beta

MCQ▾

Question

If λ is the mode of Beta(α,β)distribution given α>1andβ>1 , then which of the following relation is correct:

Choices

Choice (4) Response
a.

λ=α1α+β1

b.

λ=α+1α+β+2

c.

λ=α1α+β2

d.

λ=α+1α+β2

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