Probability-Probability Distributions (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 88 - 89 of 109

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Question number: 88

» Probability » Probability Distributions » Beta

MCQ▾

Question

A company produces bulbs that have a probability X of being defective. The manufacturer does not know X , but from past experience he expects this probability to be equal to 5% . Furthermore, he quantifies his uncertainty about X by attaching a standard deviation of 3% to his 5% estimate. After consulting with an expert in statistics, the manufacturer decides to use a Beta distribution to model her uncertainty about X . What values of parameter (α,β) will he use for making his assumptions true?

Choices

Choice (4) Response

a.

α=4.65,β=88.35

b.

α=2.59, β = 49.21

c.

α=3.82,β=72.58

d.

Question does not provide sufficient data or is vague

Question number: 89

» Probability » Probability Distributions » Beta

MCQ▾

Question

Suppose X~Beta(α,β),α>0andβ>0. Suppose Y is a random variable such that the conditional distribution of Y given X=xϵ(0, 1) is negative binomial with stopping parameter kN+ and success parameter p . Then conditional distribution X given Y=n follows ________.

Choices

Choice (4) Response

a.

Normal(α+k,β+nk)

b.

Beta(α,β+n)

c.

Beta(α+k,β+n)

d.

None of the above

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