# ISS (Statistical Services) Statistics Paper III: Questions 60 - 65 of 109

Access detailed explanations (illustrated with images and videos) to **109** questions. Access all new questions- tracking exam pattern and syllabus. View the complete topic-wise distribution of questions. *Unlimited Access, Unlimited Time, on Unlimited Devices*!

View Sample Explanation or View Features.

Rs. 300.00 -OR-

How to register? Already Subscribed?

## Question 60

Appeared in Year: *2013*

### Describe in Detail

Essay▾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 with reference to the base year

= Total of the prices of the current year

= Total of the…

… (199 more words) …

## Question 61

Appeared in Year: *2012*

### Describe in Detail

Essay▾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,

… (i)

Which is a (homogeneous) linear difference equation of order 2 in the trial solution gives

is the general solution of (i) , A and B being arbit…

… (21 more words) …

## Question 62

Appeared in Year: *2012*

### Write in Short

Short Answer▾Discuss Engel ′ s law and Engel ′ s curve. Explain Engel ′ s curve for constant price.

## Question 63

Appeared in Year: *2012*

### Describe in Detail

Essay▾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 each of the stratum such that n = , and this sample is the stratified random sample of size n .

**Allocation of a sample to d…**

… (184 more words) …

## Question 64

Appeared in Year: *2012*

### Write in Short

Short Answer▾Show that for a simple random sample unbiased estimate of

## Question 65

Appeared in Year: *2012*

### Write in Short

Short Answer▾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