### Chapter 7, Survey Sampling

#### Solution 28

#### (a)

#### (b)

In part (a), we know and as well as (known from the structure of the randomized device). Thus we can get .

#### (c)

Let if member of the random sample answers yes. Then . Thus .

Lets propose as an estimate of . Since it is a linear expression in , it follows that which is same as .

#### (d)

Since is a bernoulli’s trial, .

We have . Now, . Thus .

Putting the values in , we get . Approximating , we get: .

TODO: Not sure how if the extra term can be ignored using finite population correction as expected from the answer.