Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 135 - 136 of 205

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Question number: 135

» Probability » Probability Distributions » Beta

MCQ▾

Question

Suppose X~Beta(α,β) where α>0andβ>0 . Then which of the following statement is correct?

Choices

Choice (4) Response
a.

Then the distribution is a two-parameter exponential family with natural parameters α and β , and natural statistics X and 1X .

b.

Then the distribution is a two-parameter exponential family with natural parameters α1 and β1 , and natural statistics lnX and ln(1X) .

c.

Then the distribution is a two-parameter exponential family with natural parameters α and β , and natural statistics lnX and ln(1X) .

d.

Then the distribution is a two-parameter exponential family with natural parameters α1 and β1 , and natural statistics X and 1X .

Question number: 136

» Probability » Probability Distributions » Lognormal

MCQ▾

Question

Maximum Likelihood estimator of lognormal distribution for a series of Xis(i=1, 2,,n) with parameters μR and σ(0,) are________.

Choices

Choice (4) Response
a.

μ^=i=1nln(Xi)n and σ2^=i=1n(ln(Xi)i=1nln(Xi)n)2n

b.

μ^=i=1nln(Xi) and σ2^=i=1n(exp(Xi)i=1nln(Xi))2n

c.

μ^=i=1nln(Xi)2n and σ2^=i=1n(ln(Xi)i=1nln(Xi)2n)2n

d. None of the above

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