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

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Question number: 1

» Probability » Characteristic Function

MCQ▾

Question

Let random variables Xk=P(λk) , k=1,,n be independent Poisson random variables. So if X=i=inXn then, which of the following is the characteristic function of X if =i=inλi ?

Choices

Choice (4) Response

a.

eλeit

b.

eλ(eit+1)

c.

eλ(eit1)

d.

All of the above

Question number: 2

» Probability » Characteristic Function

MCQ▾

Question

For any random variable X , its characteristic function X(.) is uniformly continuous on R and satisfies following properties________ always.

Choices

Choice (4) Response

a.

X(t)=X(t)¯ , where for z a complex number, z¯ denote the conjugate.

b.

X(t)1

c.

X(0)=12

d.

None of the above

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