ISS Statistics Paper II (New 2016 MCQ Pattern): Questions 73 - 77 of 246

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Question number: 73

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

MCQ▾

Question

Consider a population having the density function 2α2(αx),0<x<α . Maximum Likelihood Estimators MLE of the parameter α is given by

Choices

Choice (4) Response

a.

2x

b.

α2

c.

x

d.

α

Question number: 74

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

MCQ▾

Question

Let x1,x2,,xn be a sample of independent observations from the uniform distribution on (θ, θ+1), where the value of the parameter θ is unknown (<θ<). Then the maximum Likelihood Estimator of θ is

Choices

Choice (4) Response

a.

Not unique

b.

θ^=x¯

c.

Unique

d.

None of the above

Question number: 75

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

MCQ▾

Question

In a random sampling from Normal population N(μ,σ2) the Maximum Likelihood estimator for, is

Choices

Choice (4) Response

a.

μ^=x¯

b.

μ^=nx¯

c.

μ^=2x¯

d.

μ^=x¯n

Question number: 76

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

MCQ▾

Question

Maximum Likelihood Estimators (MLE) of the parameter λ of a Poisson distribution is

Choices

Choice (4) Response

a.

MLE(λ)=λx¯

b.

MLE(λ)=x¯

c.

MLE(λ)=2x¯

d.

MLE(λ)=nx¯

Question number: 77

» 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 c is

Choices

Choice (4) Response

a.

c^=12(x¯1+x¯2+x¯3+x¯4)

b.

c^=14(x¯1+x¯2x¯3x¯4)

c.

c^=14(x¯1x¯2+x¯3x¯4)

d.

c^=14(x¯1x¯2x¯3x¯4)

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