Statistical Inference and Hypothesis Testing-Estimation Methods of Maximum Likelihood (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 30 - 32 of 35

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Question number: 30

» Statistical Inference and Hypothesis Testing » Estimation Methods of Maximum Likelihood

MCQ▾

Question

Let x1,x2,,xn denote a random sample of size n from a uniform population with p. d. f.

f(x,θ)=1;θ12xθ+12,<θ< . The MLE of θ is

Choices

Choice (4) Response

a.

MLE is Unique

b.

MLE lies between xn12(x1,x2,,xn)x1+12

c.

MLE does not exists

d.

All of the above

Question number: 31

» Statistical Inference and Hypothesis Testing » Estimation Methods of Maximum Likelihood

MCQ▾

Question

A sample of size n is drawn from each of the four a normal populations which have the same variance σ2 . the means of the four populations are +b+c , a+bc , ab+c and abc . The MLE of b is

Choices

Choice (4) Response

a.

b^=14(x¯1+x¯2x¯3x¯4)

b.

b^=12(x¯1+x¯2+x¯3+x¯4)

c.

b^=12(x¯1+x¯2+x¯3+x¯4)

d.

b^=14(x¯1x¯2x¯3x¯4)

Question number: 32

» Statistical Inference and Hypothesis Testing » Estimation Methods of Maximum Likelihood

MCQ▾

Question

Let x1,x2,,xn be a random sample from the distribution with pdf

f(x,θ)=1θe(xθ) ; 0<x< , 0<θ< , the MLE of θ is

Choices

Choice (4) Response

a.

Doesnotexists

b.

θ^=1x¯

c.

θ^=x¯

d.

θ^=2x¯

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