# ISS (Statistical Services) Statistics Paper II (New 2016 MCQ Pattern): Questions 36 - 40 of 253

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## Question number: 36

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MCQ▾

### Question

Let be a random sample of size n with mean and variance Then which of the following statements is true?

### Choices

Choice (4) Response

a.

The sample mean and sample variance are biased estimators

b.

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

c.

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

d.

None of the above

## Question number: 37

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MCQ▾

### Question

Bias of an estimator can be:

### Choices

Choice (4) Response

a.

Zero

b.

Positive

c.

Negative

d.

Both b. and c. are correct

## Question number: 38

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MCQ▾

### Question

If is a random sample from a normal distribution . Then the unbiased estimator of is

### Choices

Choice (4) Response

a.

b.

c.

d.

μ

## Question number: 39

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MCQ▾

### Question

If are random observations on a Bernoulli variate X taking the value 1 with probability and the value 0 with the probability then is a Consistent estimator of . This statement is

### Choices

Choice (4) Response

a.

True

b.

False

c.

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

d.

Question does not provide sufficient data or is vague

## Question number: 40

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MCQ▾

### Question

Let be a random sample of size n = 3 from a distribution with mean and variance . Then is a unbiased estimator of

### Choices

Choice (4) Response

a.

b.

c.

d.

None of the above