Probability-Inversion (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 1 - 2 of 3

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Question number: 1

» 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

Question number: 2

» Probability » Inversion

MCQ▾

Question

Let (.) be the characteristic function of a probability measure μ on R . If a<b, then the inversion formula is ________.

Choices

Choice (4) Response

a.

limT12πTTeit(ab)it(t)dt=μ({a})μ({b})2

b.

limT12πTTeitaeitbit(t)dt=μ((a,b))+μ({a})+μ({b})2

c.

limT12πTTeitaeitbit(t)dt=μ((a,b))+μ({a})μ({b})2

d.

limT12πTTeit(ab)it(t)dt=μ((a,b))

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