# ISS (Statistical Services) Statistics Paper III: Questions 47 - 51 of 109

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## Question number: 47

» Sampling Techniques » Probability Sampling or Random Sampling

Appeared in Year: 2011

### Describe in Detail

Discuss Lahiri’s method of selecting samples for PPS scheme. Give a suitable example to select

4 units when N = 10, M = 60, by taking your choice of sample number and its corresponding size.

### Explanation

**Lahiri’s Method of selecting samples for PPS scheme:**

Let M = max maximum of the sizes of N units in the population (i = 1,2, …10)

Steps involved in selecting samples:

1) Select a random number i from 1 to N

2) Select one more random number j, such that

3) If , then i^{th} unit is selected, otherwise the pair (i, j) is rejected and

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## Question number: 48

» Applied Statistics » Index Numbers » Income Distribution-Pareto and Engel Curves

Appeared in Year: 2011

### Describe in Detail

Explain the formulation of the problem of distribution of income. Further discuss its Mathematical formulation in order to find number of persons with income x or more.

### Explanation

Formulation of the problem of distribution of income:

The problem of distribution of income can be formulated as follows

(a) Determation of the form of the frequency distribution ϕ (x), for the total distribution of income from the poorest to the richest members of the society.

(b) Check whether ϕ (x) is governed by the society from which income is de

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## Question number: 49

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2010

### Write in Short

What is PPS Sampling? Explain why such type of sampling is needed? Describe Lahiri’s method for PPS selection of sample.

## Question number: 50

» Sampling Techniques » Cluster Sampling with SRS - Intra-Class Correlation Coefficient

Appeared in Year: 2011

### Describe in Detail

Discuss cluster sampling. Let be the sample mean based on a sample of nM elements. is the sample mean based on a sample of nM elements drawn for SRS without replacement from NM elements in the population. Obtain Relative efficiency of with respect to (without getting the derivation of V ( ) and V ( ) ). Write its ANOVA table.

### Explanation

Cluster sampling:

Cluster sampling is a type of sampling method. If the population size is very large, the samplings lead to several difficulties. It might be tough to prepare a frame for large population size. In such case the, cluster sampling is used. In this method, the population is divided into separate groups, called clusters. Then, a simple

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## Question number: 51

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

### Describe in Detail

Let , - ∞ < t < ∞, where are i, i. d. with and . Show that the process is stationary with correlation.

### Explanation

It is given that

→ ……………. (i)

using (i)

Similarly, we will get

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