Probability-Probability Distributions (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 75 - 77 of 109

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Question number: 75

» Probability » Probability Distributions » Joint and Marginal Distributions

MCQ▾

Question

If f(x,y)=c(x2+y2) is the density function for the joint distribution of the continuous random variables X and Y defined over the unit square bounded by the points (0, 0),(0, 1),(1, 0) and (1, 1), then the value of c is ________.

Choices

Choice (4) Response
a.

23

b.

32

c.

12

d. None of the above

Question number: 76

» Probability » Probability Distributions » Random Vectors

MCQ▾

Question

The joint density function of two continuous random variables X and Y is

f(x,y)={

What is the value of P(1<X<2, 2<Y<3) ?

Choices

Choice (4) Response
a.

3192

b.

796

c.

5126

d. None of the above

Question number: 77

» Probability » Probability Distributions » Gamma

MCQ▾

Question

Which of the following statements is/are correct regarding Gamma distribution with (α,β) parameters?

Choices

Choice (4) Response
a.

If X1,X2,,Xn represents identically distributed, independent gamma random variables with parameters α and β , then if Y=i=1nXi , E(Y)=nαβV(Y)=nαβ2

b.

If X1,X2,,Xn represents identically distributed, independent gamma random variables with parameters α and β , then Y=i=1nXi also have a gamma distribution with parameters nα and β .

c.

If α=1, the gamma density function is reduced to the exponential density function.

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

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