# ISS (Statistical Services) Statistics Paper III: Questions 60 - 65 of 96

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## Question number: 60

» Applied Statistics » Index Numbers » Laspeyre

Appeared in Year: 2013

### Describe in Detail

Discuss simple aggregate method of Index number. Why is weighted average of price relative index preferred over simple aggregate method? Show that weighted average of price relative index number is same as that of Paasche’s index number.

### Explanation

**Simple aggregate method of Index number: **

This method consists of expressing aggregate of prices in any year as a percentage of their aggregate i^{th} the base year. The price index, under this method is computed by the formula

Where

= Price index of the current year

## Question number: 61

» Applied Statistics » Periodogram and Correlogram Analyses

Appeared in Year: 2012

### Describe in Detail

Obtain the correlogram for the series with, provided, , and successive values of are independent.

### Explanation

It is given that

And hence

Substituting the value in we get,

Where ηs are independent.

Multiplying both sides of the above equation by , taking expectations and dividing by , we get for a long series,

## Question number: 62

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

Appeared in Year: 2012

### Write in Short

Discuss Engel’s law and Engel’s curve. Explain Engel ’s curve for constant price.

## Question number: 63

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2012

### Describe in Detail

Discuss the allocation of a sample to different strata in stratified sampling. Explain proportional allocation and hence obtain the variance of mean of a stratified sample under proportional allocation.

### Explanation

For a population consisting of N sampling units it can be divided into k relatively homogeneous sub-groups of sizes, , …, (called as strata) such that N=.

Then a simple random sample of size (i = 1, 2, …, k) is drawn from

## Question number: 64

» Sampling Techniques » Simple Random Sampling With and Without Replacement

Appeared in Year: 2012

### Write in Short

Show that for a simple random sample unbiased estimate of

## Question number: 65

» Econometrics » Ordinary Least Squares (OLS)

Appeared in Year: 2012

### Write in Short

If the demand curve is of the form , where *p* is the price and *x* is the demand, prove that the elasticity of demand is · Hence deduce the elasticity of demand for