Probability-Probability Distributions (ISS (Statistical Services) 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: Equation for Equation and Equation . What is the conditional density of Equation given Equation ?

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Question number: 91

» Probability » Probability Distributions » Gamma

MCQ▾

Question

If Equation has the gamma distribution with shape parameter Equation then it’s moment generating function is ________ Equation .

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Question number: 92

» Probability » Probability Distributions » Joint and Marginal Distributions

MCQ▾

Question

Continuous random variables Equation and Equation have a joint distribution with density function

Equation in the region bounded by Equation Find the density function for the marginal distribution of Equation for Equation

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Question number: 93

» Probability » Probability Distributions » Beta

MCQ▾

Question

Suppose Equation where Equation . 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 Equation and Equation , and natural statistics Equation and Equation .

b.

Then the distribution is a two-parameter exponential family with natural parameters Equation and Equation , and natural statistics Equation and Equation .

c.

Then the distribution is a two-parameter exponential family with natural parameters Equation and Equation , and natural statistics Equation and Equation .

d.

Then the distribution is a two-parameter exponential family with natural parameters Equation and Equation , and natural statistics Equation and Equation .

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