# ISS (Statistical Services) Statistics Paper III: Questions 12 - 16 of 109

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## Question 12

Appeared in Year: *2015*

### Describe in Detail

Essay▾What are the advantages of stratified sampling? Consider the allocation of sample size n_{i} of strata given by , where N_{i} is the stratum size, σ_{i} is the within stratum standard deviation of the ith stratum, (i = 1,2, … , k) and δ real. Write down the expression for the where stands for the unbiased estimator of the population mean of the study variate y based on sample random sample without replacement in each stratum.

### Explanation

In this type of sampling method first the whole population is divided into homogeneous groups under certain criterion. There groups are termed as strata. Many advantage of stratified sampling can be summarized as follows.

(i) if the admissible error is given, small samples is needed which results into a cut of expenditure.

(ii) In case the cost of su…

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## Question 13

Appeared in Year: *2015*

### Describe in Detail

Essay▾Describe in detail Indirect Least square method for estimating structural parameters. Is the estimator unbiased and/or consistent?

### Explanation

For a just or exactly identified structural equation, the method of obtaining the estimates of the structural coefficients from the OLS estimates of the reduced-form coefficients is known as the method of indirect least squares (ILS) , and the estimates thus obtained are known as the indirect least squares estimates. ILS involves the following thre…

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## Question 14

Appeared in Year: *2015*

### Describe in Detail

Essay▾Describe exact and near multicollinearity in a regression model. Discuss, along with justification, the effect of these situations on (i) sampling variation and (ii) prediction.

### Explanation

Multicollinearity refers to the existence of a perfect or exact linear relationship among some or all explanatory variables of a regression model. So, there are two types of multicollinearity. They are

1. **Exact Multicollinearity**: If exist perfect linear relationship among the explanatory variables then it is treated as exact multicollinearity. In ca…

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## Question 15

Appeared in Year: *2009*

### Write in Short

Short Answer▾Explain the time reversal and factor-reversal tests for an ideal index number. Give an example

of index number which satisfies both of these tests.

## Question 16

Appeared in Year: *2009*

### Describe in Detail

Essay▾State the probability density function of the Pareto distribution and give its cumulative form.

Interpret the constants involved.

### Explanation

**Probability Density Function of the Pareto distribution**:

Suppose that X has the Pareto distribution with shape parameter a ∈ (0, ∞) and scale parameter b ∈ (0, ∞) then X has probability density function f given by

where is the (necessarily positive) minimum possible value of X, and α is a positive parameter.

Pareto Type I distribution is characterize…

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