ISS Statistics Paper II (New 2016 MCQ Pattern): Questions 35 - 39 of 246

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Question number: 35

» Statistical Inference and Hypothesis Testing » Characteristics of Good Estimator

MCQ▾

Question

Let X1,X2,X3 be a random sample of size n = 3 from a distribution with mean μ and variance σ2 . If T1=X1+X2X3 , T2=2X1+3X34X2 and T3=X1+X2+X33 . Which one is the best estimator in terms of variance?

Choices

Choice (4) Response
a.

T2

b.

T1

c.

T3

d. Question does not provide sufficient data or is vague

Question number: 36

» Statistical Inference and Hypothesis Testing » Characteristics of Good Estimator

MCQ▾

Question

Let x1,x2,,xn be a random sample of size n with mean μ and variance σ2. Then which of the following statements is true?

Choices

Choice (4) Response
a.

The sample mean and sample variance are unbiased estimators of the mean and variance of the underlying distribution.

b.

Sample mean is unbiased estimator and sample variance is biased estimator.

c.

The sample mean and sample variance are biased estimators

d. All of the above

Question number: 37

» Statistical Inference and Hypothesis Testing » Characteristics of Good Estimator

MCQ▾

Question

Bias of an estimator can be:

Choices

Choice (4) Response
a.

Positive

b.

Negative

c.

Zero

d. Both a. and b. are correct

Question number: 38

» Statistical Inference and Hypothesis Testing » Characteristics of Good Estimator

MCQ▾

Question

If x1,x2,,xn is a random sample from a normal distribution N(μ;1) . Then the unbiased estimator of t=1ni=1nxi2 is

Choices

Choice (4) Response
a.

μ2

b.

μ21

c.

μ

d.

μ2+1

Question number: 39

» Statistical Inference and Hypothesis Testing » Characteristics of Good Estimator

MCQ▾

Question

If X1,X2,.,Xn are random observations on a Bernoulli variate X taking the value 1 with probability p and the value 0 with the probability (1p) then xin(1xin) is a Consistent estimator of p(1p) . This statement is

Choices

Choice (4) Response
a.

Since X is not a consistent estimator of p , this is false.

b.

False

c.

True

d. None of the above

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