# Statistical Inference and Hypothesis Testing (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 219 - 220 of 222

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## Question number: 219

» Statistical Inference and Hypothesis Testing » Sufficient Estimator

MCQ▾

### Question

Which of the definition is true for Sufficiency of an estimator?

### Choices

Choice (4) Response

a.

A statistic is sufficient estimator of parameter if and only if the likelihood function (joint p. d. f. of the sample) can be expressed as where is the p. d. f. of statistic and is a function of sample observations only independent of

b.

If is a estimator of parameter based on a sample of size n from the population with density such that the conditional distribution of given T is independent of then T is sufficient estimator of .

c.

An estimator is said to be sufficient for if it provides all the information contained in the sample about the parametric function

d.

All a. , b. and c. are correct

## Question number: 220

» Statistical Inference and Hypothesis Testing » Cramer-Rao Inequality

MCQ▾

### Question

Cramer-Rao Inequality provides a Lower bond to the variance of an ________ estimator for a parameter.

### Choices

Choice (4) Response

a.

Unbiased

b.

Consistent

c.

Maximum Likelihood estimator

d.

Sufficient