ISS Statistics Paper I (New 2016 MCQ Pattern): Questions 314 - 315 of 404

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Question number: 314

» Probability » Modes of Convergences of Sequences of Random Variables » In Distribution

MCQ▾

Question

Consider a random permutation (X1,X2,,Xn) of the elements in the set {1, 2,,n} . We say that s match occurs at position iifXi=i . If Nn denotes the number of matches, then the distribution of Nn converges to ________ as n .

Choices

Choice (4) Response

a.

Exponential distribution with parameter 1

b.

Poisson distribution with parameter 1

c.

Laplace distribution with location parameter 0 and scale parameter 1

d.

None of the above

Question number: 315

» 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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