ISS Statistics Paper III: Questions 74 - 80 of 90

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Question number: 74

» Sampling Techniques » Probability Sampling or Random Sampling

Appeared in Year: 2012

Short Answer Question▾

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

Essay Question▾

Describe in Detail

Obtain the complementary function and particular integral of first order regressive model. Show that Equation is a moving average of random elements with weights, Equation

Explanation

Let us consider the first order auto regressive model

Equation ……. . (i)

this is a linear difference equation of order 1. its complementary function (C. F. ) is the so; ution of

Equation

which is a homogeneous linear difference equation of order 1.

if Equation is the trial solution,… (117 more words) …

Question number: 76

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

Appeared in Year: 2013

Essay Question▾

Describe in Detail

In simple random sampling without replacement (SRSWOR), the sample mean Equation is an unbiased estimator of population mean Equation . Obtain the variance of the estimator of the population total Y.

Explanation

Sample mean Equation is an unbiased estimator of population mean Equation i. e.

Sample mean is given by Equation

It can also be written as Equation

Where

Equation

Equation Equation

Equation

Equation

Equation

Equation

Equation

Hence Equation

Equation

Variance of the estimator of the population total Y: Equation:

Let… (57 more words) …

Question number: 77

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

Appeared in Year: 2012

Essay Question▾

Describe in Detail

Discuss link relative method to estimate seasonal fluctuations, with appropriate illustrations.

Explanation

link relative is the value of one season expressed as a percentage of the preceding season. The word ‘season’ refers to time period, it means month for monthly data, quarter for quarterly data etc.

Under this method, the seasonal indices are found with the following steps.

Steps:

(i) Find the… (230 more words) …

Question number: 78

» Sampling Techniques » Probability Sampling or Random Sampling

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Give the names of various procedures for selecting a sample using probability proportional to size (PPS) scheme. Obtain an unbiased estimator of the population mean under PPS.

Explanation

Procedures for selecting a sample using probability proportional to size (PPS) scheme are:

  • PPS sampling with Replacement

  • PPS sampling without Replacement

  • Cumulative total method

  • Lahiri’s method

An unbiased estimator of the population mean under PPS:

Let Equation= value of the ith unit of the population, i = 1, 2,… (96 more words) …

Question number: 79

» Econometrics » Ordinary Least Squares (OLS)

Appeared in Year: 2012

Short Answer Question▾

Write in Short

Let the demand function be expressed as Equation . For what value of X, the elasticity of demand will be unitary?

Question number: 80

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Describe the principles of stratification. Explain how the allocation of sample size in different strata is made.

Explanation

Principles of stratification:

The principle of stratification is the division of the population in such a way that the elements within a stratum are as similar as possible and the means of the strata are as different as possible.

Auxiliary information (past or some other information) related to the character… (278 more words) …

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