ISS Statistics Paper II (New 2016 MCQ Pattern): Questions 45 - 48 of 246

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Question number: 45

» Statistical Inference and Hypothesis Testing » Characteristics of Good Estimator

MCQ▾

Question

If x1,x2,,xn is a random sample from a Bernoulli population with parameter θ , then [xi(xi1)]n(n1) is

Choices

Choice (4) Response

a.

An unbiased estimator of θ2

b.

A biased estimator of θ2

c.

An unbiased estimator of θ2 +1

d.

None of the above

Question number: 46

» Statistical Inference and Hypothesis Testing » Characteristics of Good Estimator

MCQ▾

Question

If Xi are normally distributed random variables with mean μ and variance σ2 , then sample variance is

Choices

Choice (4) Response

a.

Unbiased estimate of population variance σ2

b.

E(s2)σ2

c.

Not an unbiased estimate of population variance σ2

d.

Both b. and c. are correct

Question number: 47

» Statistical Inference and Hypothesis Testing » Characteristics of Good Estimator

MCQ▾

Question

Let x1,x2,,xn be a random sample from a uniform population on [0, θ ]. Then the sufficient estimator for θ is

Choices

Choice (4) Response

a.

T=max{x1,x2,,xn}

b.

T=min{x1,x2,,xn}

c.

Question does not provide sufficient data or is vague

d.

All of the above

Question number: 48

» Statistical Inference and Hypothesis Testing » Characteristics of Good Estimator

MCQ▾

Question

A random sample X1,X2,X3,X4,X5 of size 5 is drawn from a normal population with mean μ and σ2 . And if T1=X1+X2+X3+X4+X55 , T2=X1+X22+X3 , T3=2X1+X23 Which one is the best estimator in terms of variance?

Choices

Choice (4) Response

a.

T2

b.

T3

c.

T1

d.

All of the above

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