Probability-Moment and Probability Generating Functions (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 1 - 4 of 7

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Question number: 1

» Probability » Moment and Probability Generating Functions

MCQ▾

Question

For a random variable X , if we have the moment generating function MX(s)=22s , for s(2, 2) . Then the distribution of X is ________.

Choices

Choice (4) Response
a.

X~Exponential(2)

b.

X~Normal(0, 2)

c.

X~Poission(2)

d. Question does not provide sufficient data or is vague

Question number: 2

» 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: 3

» 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

Question number: 4

» Probability » Moment and Probability Generating Functions

MCQ▾

Question

Suppose that X and Y are independent random variables taking values in N, with probability generating functions P1 and P2 having radii of convergence r1 and r2 , respectively. Then the probability generating function P of X+Y is given by________ for t <r1 r2 .

Choices

Choice (4) Response
a.

P(t)=P1(t)+P2(t)

b.

P(t)=P1(t)P2(t)

c.

P(t)=P1(t)P2(t)

d. None of the above

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