# ISS (Statistical Services) Statistics Paper III: Questions 74 - 79 of 109

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## Question 74

Appeared in Year: *2012*

### Write in Short

Short Answer▾Obtain an unbiased estimator of the gain due to PPSWR sampling as compared to SRSWR.

## Question 75

Appeared in Year: *2013*

### Describe in Detail

Essay▾Obtain the complementary function and particular integral of first order regressive model. Show that ** is a moving average of random elements with weights, **

### Explanation

Let us consider the first order auto regressive model

… (i)

this is a linear difference equation of order 1. its complementary function (C. F.) is the so; ution of

which is a homogeneous linear difference equation of order 1.

if is the trial solution, then

ignoring the trivial solution

Hence complementary function (C. F) is

From (i) , E is the differ…

… (71 more words) …

## Question 76

Appeared in Year: *2013*

### Describe in Detail

Essay▾In simple random sampling without replacement (SRSWOR) , the sample mean ** is an unbiased estimator of population mean ****. Obtain the variance of the estimator of the population total Y.**

### Explanation

Sample mean is an unbiased estimator of population mean i.e..

Sample mean is given by

It can also be written as

Where

Hence

**Variance of the estimator of the population total Y**: :

Let us denote the Population Total Y as

The estimate of population total Y can be obtained by multiplying the estimate of mean by population size N.

Estimator of populatio…

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## Question 77

Appeared in Year: *2012*

### Describe in Detail

Essay▾Discuss link relative method to estimate seasonal fluctuations, with appropriate illustrations.

### Explanation

link relative is the value of one season expressed as a percentage of the preceding season. The word ‘season’ refers to time period, it means month for monthly data, quarter for quarterly data etc.

Under this method, the seasonal indices are found with the following steps.

**Steps**:

(i) Find the link relative of all the seasonal data using the formulae

W…

… (202 more words) …

## Question 78

Appeared in Year: *2013*

### Describe in Detail

Essay▾Give the names of various procedures for selecting a sample using probability proportional to size (PPS) scheme. Obtain an unbiased estimator of the population mean under PPS.

### Explanation

**Procedures for selecting a sample using probability proportional to size (PPS) scheme are**:

- PPS sampling with Replacement
- PPS sampling without Replacement
- Cumulative total method
- Lahiri՚s method

**An unbiased estimator of the population mean under PPS**:

Let = value of the ith unit of the population , i = 1,2, … , N

= known value of the auxiliary variable fo…

… (71 more words) …

## Question 79

Appeared in Year: *2012*

### Write in Short

Short Answer▾Let the demand function be expressed as . For what value of X, the elasticity of demand will be unitary?