ISS (Statistical Services) Statistics Paper III: Questions 74 - 79 of 109
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Question 74
Appeared in Year: 2012
Write in Short
Short Answer▾Obtain an unbiased estimator of the gain due to PPSWR sampling as compared to SRSWR.
Question 75
Appeared in Year: 2013
Describe in Detail
Essay▾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 complementary function (C. F) is
From (i) , E is the differ…
… (71 more words) …
Question 76
Appeared in Year: 2013
Describe in Detail
Essay▾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 us denote the Population Total Y as
The estimate of population total Y can be obtained by multiplying the estimate of mean by population size N.
Estimator of populatio…
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Question 77
Appeared in Year: 2012
Describe in Detail
Essay▾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 link relative of all the seasonal data using the formulae
W…
… (202 more words) …
Question 78
Appeared in Year: 2013
Describe in Detail
Essay▾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, … , N
= known value of the auxiliary variable fo…
… (71 more words) …
Question 79
Appeared in Year: 2012
Write in Short
Short Answer▾Let the demand function be expressed as . For what value of X, the elasticity of demand will be unitary?