# ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern): Questions 30 - 32 of 39

Access detailed explanations (illustrated with images and videos) to 39 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. Subscription can be renewed yearly absolutely FREE! View Sample Explanation or View Features.

Rs. 200.00 or

How to register?

## Question number: 30

» Estimation » Optimal Properties » Cramer-Raoinequality

Edit

Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Stating the regularity conditions, give the Cramer-Rao lower bound for the variance of an unbiased estimator of a parameter. Give an example, each, of a situation where the regularity conditions (i) does not hold (ii) holds

### Explanation

Suppose that X 1, …, X n is a sample from a distribution with joint pdf f n (x, θ) and T (X) is an estimator. Also assume that f n () satisfies the conditions that allow

(i) Interchange of differentiation and integration operations i. e.

… (150 more words) …

## Question number: 31

» Estimation » Optimal Properties » Rao-Blackwell Theorem

Edit

Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Explain how the Rao-Blackwell theorem helps one to find a uniformly minimum variance unbiased estimator (UMVUE) of an unknown parameter. What is the relevance of the Lehman-Scheffe theorem in this scenario? If X 1, X 2, …, X n are Bin (1, p) variates, find the UMVUE of p.

### Explanation

Let U be an unbiased estimator of θ and T be a sufficient statistic for θ, then E (U|T) is free from θ and it is an estimation. Using the identity , we have

True for all θ. Then is an unbiased f

… (157 more words) …

## Question number: 32

» Statistical Quality Control » Control Charts » Variable

Edit

Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Sample of sizes n = 5 are taken from a manufacturing process every hour. A quality characteristic is measured, and and R are computed for each sample. After 25 samples have been analyzed, we have and . Assume that the quality characteristic is normally distributed.

(i) Find the control limit for the and R charts.

(ii) Assume that both chart exhibit control, if specifications are 26.40±0.50, estimate the fraction nonconforming. Express your answers in terms of CDF of N (0,1) random variable.

[For n = 5, A 2 =0.577, A = 1.342, A 3 =1.427, D 1 =0, D 2 =4.918, D 3 =0, D 4 =2.115 and d 2 =2.326]

### Explanation

Given that and

(i) For chart, the control limits are

… (103 more words) …