Probability-Moment and Probability Generating Functions (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 5 - 7 of 7

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Question number: 5

» Probability » Moment and Probability Generating Functions

MCQ▾

Question

A hen lays N eggs, where N~Poission(λ) . Each egg hatches with probability p , independently of the other eggs. Find the probability distribution of number of chicks, Z.

Choices

Choice (4) Response

a.

Z~Poission(λp)

b.

Z~Poission(λ)

c.

Z~NegativeBinomial(n,p)

d.

Question does not provide sufficient data or is vague

Question number: 6

» Probability » Moment and Probability Generating Functions

MCQ▾

Question

Suppose that N is a random variable taking values in N. The probability generating function P of N will satisfy the following properties.

Choices

Choice (4) Response

a.

P(Niseven)=12[P(1)P(1)]

b.

P(Niseven)=12[1+P(1)]

c.

P(Niseven)=12[1P(1)]

d.

All of the above

Question number: 7

» Probability » Moment and Probability Generating Functions

MCQ▾

Question

If X~Binomial(m,p) and Y~Binomial(n,p) are independent, then what is the distribution of +Y ?

Choices

Choice (4) Response

a.

X+Y~Binomial(mn,p)

b.

X+Y~Binomial(mn,p)

c.

X+Y~Binomial(mn,p)

d.

None of the above

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