# Sampling Techniques-Multistage Sampling and Its Application (ISS (Statistical Services) Statistics Paper III): Questions 1 - 1 of 1

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## Question number: 1

» Sampling Techniques » Multistage Sampling and Its Application

Appeared in Year: 2015

### Describe in Detail

Consider a population U= {u _{1}, u _{2}, …, u _{n}}. Observations of study variable (y) and auxiliary variable (x) are y (u _{i}) =y _{i}, x (u _{i}) =x _{i}, i = 1, 2, . . , N. Let p _{i} =X _{i} /X where . A sample of size n is drawn with PPSWR. Show that the population total , the estimator is an unbiased estimator. Obtain the variance of the estimator of the population total.

### Explanation

Consider a population U= {u _{1}, u _{2}, …, u _{n}}. Observations of study variable (y) and auxiliary variable (x) are y (u _{i}) =y _{i}, x (u _{i}) =x _{i}, i = 1, 2, . . , N. Let p _{i} =X