The number of detections in a radar resolution cell is a binary random variable X having the probabilities P{X = 1} = p and P{X = 0} = 1 - p with unknown p.

(a) Find the mean and variance of X in terms of p.

(b) Given a sample {1,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0} of X, find the sample mean X^.

(c) What are the mean and variance of X^ in terms of p?

(d) What is your best guess (call it p^) of the unknown p? What is your best guess E[(p^ - p)^2]?