ISS (Statistical Services) Statistics Paper III: Questions 74  80 of 96
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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,
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
Hence
Variance of the estimator of the population total Y: :
Let
Question number: 77
» Applied Statistics » Time Series Analysis » Determination of Trend, Seasonal and Cyclical Fluctuations
Appeared in Year: 2012
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
Question number: 78
» Sampling Techniques » Probability Sampling or Random Sampling
Appeared in Year: 2013
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 = value of the ith unit of the population, i = 1, 2,
Question number: 79
» Econometrics » Ordinary Least Squares (OLS)
Appeared in Year: 2012
Write in Short
Let the demand function be expressed as. For what value of X, the elasticity of demand will be unitary?
Question number: 80
» Sampling Techniques » Stratified Random Sampling
Appeared in Year: 2013
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.
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