Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 168 - 171 of 205

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Question number: 168

» 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: 169

» Probability » Mathematical Expectation and Conditional Expectation

MCQ▾

Question

Let X and Y be independent; each is uniformly distributed on [0, 1]. Let Z=X+Y , then E[XZ X]= ________.

Choices

Choice (4) Response

a.

X+12

b.

12

c.

1

d.

X(X+12)

Question number: 170

» Probability » Moment and Probability Generating Functions

MCQ▾

Question

If X and Y are independent discrete random variables with the non-negative integers {0, 1,2, 3,} as range, and with distribution function pX(j)=pY(j)=qjp then, what is the distribution of Z=X+Y ?

Choices

Choice (4) Response

a.

Poission distribution

b.

Geometric distribution

c.

Negative binomial distribution

d.

None of the above

Question number: 171

» Probability » Moment and Probability Generating Functions

MCQ▾

Question

Let N,X1,X2, be independent count r. v. s. If the {Xi} are identically distributed, each with Probability generating function GX then SN=X1++Xn has Probability generating function________.

Choices

Choice (4) Response

a.

GX(GN(s))

b.

GN(GX(s))

c.

E[GX(s)]

d.

None of the above

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