# ISS (Statistical Services) Statistics Paper III: Questions 69 - 76 of 109

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## Question number: 69

» Econometrics » Prediction and Simultaneous Confidence Intervals

Appeared in Year: 2012

### Write in Short

Discuss forecasting accuracy and Theil’s U coefficient.

## Question number: 70

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

Appeared in Year: 2012

### Write in Short

Using curves of concentration, discuss the formulation of the problem of distribution of income.

## Question number: 71

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2012

### Write in Short

Obtain the general solution of first-order auto-regression model.

## Question number: 72

» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process

Appeared in Year: 2013

### Describe in Detail

Discuss the relevance of variate difference method in time series analysis data. Show that

### Explanation

**Relevance of variate difference method: **

Although many different formulas are used to measure the random component in a time series, , the variate difference method fits the best, because this method method enables us to estimate the variance of the random component in a series. The variate difference method does not require the specification of a

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## Question number: 73

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2013

### Describe in Detail

Explain circular systematic sampling. Show that minimum value of ρ is** , **when **, **where ρis intraclass correlation and** **is the sample mean.

### Explanation

**Circular systematic sampling**

This method consists of choosing a random start from 1 to N and selecting the unit corresponding to the random start and thereafter every k^{th} unit in a cyclic manner till a sample of size n units is obtained, k being the integer nearest to .

That is, if r is the number selected at random from 1 to N, the sample cons

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## Question number: 74

» Sampling Techniques » Probability Sampling or Random Sampling

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

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2013

### 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 trial solution, then

ignoring the trivial solution

Hence

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## Question number: 76

» Sampling Techniques » Simple Random Sampling and Sampling with Probability Proportional to Size

Appeared in Year: 2013

### 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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