Statistical Inference and Hypothesis Testing (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 58 - 61 of 222

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Question number: 58

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

MCQ▾

Question

The MLE of the parameter α of the distribution 1Γ(λ)(λα)λeλxαxλ1;0x<,λ>0 is given by

Choices

Choice (4) Response

a.

MLE(α)=x¯

b.

MLE(α)=λx¯

c.

MLE(α)=2x¯

d.

MLE(α)=λx¯

Question number: 59

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

MCQ▾

Question

Consider a function θ^=(x1,x2,,xn) of the sample values. θ^ is said to be Maximum Likelihood Estimator (MLE) if

Choices

Choice (4) Response

a.

L(θ^)<L(θ)

b.

L(θ^)=L(θ)

c.

L(θ^)>L(θ)

d.

All of the above

Question number: 60

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

MCQ▾

Question

The maximum Likelihood Estimator of θ in f(x,θ)=(1+θ)xθ,0<x<1 is

Choices

Choice (4) Response

a.

Does not exists

b.

θ^=ni=1nlogxi1

c.

θ^=ni=1nlogxi1

d.

Question does not provide sufficient data or is vague

Question number: 61

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

MCQ▾

Question

The principle of Maximum Likelihood consists of finding an estimator, which ________ the likelihood function.

Choices

Choice (4) Response

a.

Minimizes

b.

Maximizes

c.

Maximizes or Minimizes

d.

All of the above

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