Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 155 - 157 of 205

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Question number: 155

» Probability » Probability Distributions » Distributions of Functions of Random Variables

MCQ▾

Question

Let X be a random variable with support x[0, 1] and distribution function

FX(x)={

Then the distribution function of Y=X2 is ________.

Choices

Choice (4) Response

a.

FY(y)={

b.

FY(y)={

c.

FY(y)={

d.

All of the above

Question number: 156

» Probability » Modes of Convergences of Sequences of Random Variables » With Probability One

MCQ▾

Question

If XnXasn in probability, then there exists a subsequence (n1,n2,n3) of N+ such that ________.

Choices

Choice (4) Response

a.

XnkX almost everywhere

b.

XnkX as k with probability 1.

c.

XnkX in the k -th mean

d.

Question does not provide sufficient data or is vague

Question number: 157

» Probability » Inversion

MCQ▾

Question

Let X be a real random variable whose characteristic function is integrable over R, so (t) dt< . Then X has a bounded continuous density f on R given by________.

Choices

Choice (4) Response

a.

f(x)=12π(t)dt

b.

f(x)=12πeitx(t)dt

c.

f(x)=12π0eitx(t)dt

d.

f(x)=12π0eitx(t)dt

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