# ISS (Statistical Services) Statistics Paper III: Questions 74 - 80 of 109

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## Question number: 74

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Appeared in Year: 2012

### Write in Short

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

## Question number: 75

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

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 tr

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## Question number: 76

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

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

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## Question number: 77

» Applied Statistics » Time Series Analysis » Determination of Trend, Seasonal and Cyclical Fluctuations

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Appeared in Year: 2012

Essay Question▾

### Describe in Detail

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 fo

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## Question number: 78

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

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

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## Question number: 79

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Appeared in Year: 2012

### Write in Short

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

## Question number: 80

Edit

Appeared in Year: 2013

Essay Question▾

### Describe in Detail

Describe the principles of stratification. Explain how the allocation of sample size in different strata is made.

### Explanation

Principles of stratification:

The principle of stratification is the division of the population in such a way that the elements within a stratum are as similar as possible and the means of the strata are as different as possible.

Auxiliary information (past or some other information) related to the character under study may be used to divide the

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