# ISS Statistics Paper III: Questions 54 - 59 of 90

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## Question number: 54

Appeared in Year: 2011

Essay Question▾

### Describe in Detail

For the auto-regressive scheme , show that if e is a random variable and the series is long, then

and hence show that, variance of the generated series may be much greater than that of e itself.

### Explanation

Given auto-regressive scheme is a second order Auto-regressive series.

……………. . (i)

Since the series is long and , we have

and Var

Squaring both sides of (i) and taking the expectations, we get

…………. . (i)

Multiplying both sides… (66 more words) …

## Question number: 55

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

Appeared in Year: 2013

Essay Question▾

### Describe in Detail

Explaining Pareto’s law of income distribution, show that the elasticity decreases in the number of persons while passing to a higher income class.

### Explanation

Pareto’s law of income distribution:

Pareto’s states that ‘the number of income recipients earning at least a given level of income would tend to fall by a fixed percentage as that given level of income rose by a fixed percentage. ’

Pareto’s law implies that inequality is inescapable and nothing… (190 more words) …

## Question number: 56

Appeared in Year: 2012

Essay Question▾

### Describe in Detail

Discuss the practical consequences of autocorrelation. Show that

### Explanation

Practical consequences of autocorrelation:

1. OLS estimators are still unbiased and consistent.

2. The variance of the estimators are underestimated. In the presence of autocorrelation , but Thus, variance of may be either over estimated or under estimated depending upon the nature of the correlation.

3. Prediction will be… (175 more words) …

## Question number: 57

Appeared in Year: 2012

### Write in Short

Show that mean of a systematic sample is more precise than the mean of a simple random sample of size n under a certain condition to be obtained by you.

## Question number: 58

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

Appeared in Year: 2013

Essay Question▾

### Describe in Detail

Discuss Engel’s curve. Explain the Engel’s curve for constant price of a demand functionwhere is national income and p is price.

### Explanation

Engel’s curve: The graphic representation of the basic relationship between household income and its expenditure on a particular item of consumption is known as Engel’s curve. The Engel curves shows the effect of a change in income on the expenditure for each good at fixed prices. If price change, the… (281 more words) …

## Question number: 59

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

Appeared in Year: 2012

Essay Question▾

### Describe in Detail

What are the different methods for measurement of trend? Discuss the method of fitting a straight line using least squares method.

### Explanation

Methods of measurement of trend:

Trend can be measured by the following methods:

(i) Graphic method or trend by Inspection

(ii) Method of Semi-Averages

(iii) Method of Curve fitting by principles of Least Squares

(iv) Method of moving averages

Fitting a straight line using least squares method:

Let be… (230 more words) …

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