Thread: Estimating a proportion

Could someone please help me with this question:

Consider the population of all people resident in a town. Let p be the proportion of these who have ever been prescribed glasses or contact lenses. An optician wants to estimate p, so she chooses a random sample of 512 residents and asks each one if they have ever been prescribed glasses or contact lenses. Let X be the number who answer “yes”.

(a) State the distribution of the random variable X. Hence write down the expectation and variance of X.

(b) Find P(X ≤ 200) if p = 1/3.

(c) Let Y = X/512. Show that Y is an unbiased estimator of p.

(d) Find the mean squared error of Y as a function of p.

Thank you!

What kind of help do you want? Someone to do the problems for you? You will be much better off if you showed what you have tried so that we can see where you had problems and what kind of hints will help.