Chapter 7, Survey Sampling

Solution 26


(a)

We need to show that . Since we have exactly terms in the sum , where , we can denote those terms by , where varies from to . Thus we have . But , it follows that .

(b)

means the probability that element of the population is present in a random sample of size n. This is equivalent to the probability of selecting an element in a random sample of size . Thus .

Since is either or , by fundamental bridge, it follows .

(c)

.

(d)

(e)

(f)

$$\tag*{$\blacksquare$} $$