Probability-Probability Distributions (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 90 - 93 of 109

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Question number: 90

» Probability » Probability Distributions » Conditional Distributions

MCQ▾

Question

Suppose the continuous random variables X and Y have the following joint probability density function: f(x,y)=32 for x2y1 and 0<x<1 . What is the conditional density of Y given =x ?

Choices

Choice (4) Response
a.

12(1x2)

b.

32(1+x2)

c.

32(1x2)

d.

1(1x2)

Question number: 91

» Probability » Probability Distributions » Gamma

MCQ▾

Question

If X has the gamma distribution with shape parameter k then it’s moment generating function is ________ ,t<1 .

Choices

Choice (4) Response
a.

t(1+t)k

b.

1(1t)k

c.

1(1+t)k

d.

t(1t)k

Question number: 92

» 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)=3(22xy)2 in the region bounded by y=0,x=0,andy=22x. Find the density function for the marginal distribution of X for 0<x<1.

Choices

Choice (4) Response
a.

3(1+x)2

b.

3(1x)2

c.

(1x)2

d.

(1x)

Question number: 93

» Probability » Probability Distributions » Beta

MCQ▾

Question

Suppose X~Beta(α,β) where α>0andβ>0 . Then which of the following statement is correct?

Choices

Choice (4) Response
a.

Then the distribution is a two-parameter exponential family with natural parameters α and β , and natural statistics X and 1X .

b.

Then the distribution is a two-parameter exponential family with natural parameters α1 and β1 , and natural statistics lnX and ln(1X) .

c.

Then the distribution is a two-parameter exponential family with natural parameters α and β , and natural statistics lnX and ln(1X) .

d.

Then the distribution is a two-parameter exponential family with natural parameters α1 and β1 , and natural statistics X and 1X .

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