. A balanced coin is flipped twice. Let Y = number of heads obtained.

a. Specify the probabilities for the possible values for Y, and give the distri- bution's mean and variance.

b. Calculate probabilities for the Poisson distribution having the same mean as the distribution in (a). How does its variance compare to that in (a)?

c. For each flip of a possibly unbalanced coin, let 7 denote the probability of a head. Suppose there are 0 heads in 2 flips. Find the ML estimate of . Does this estimate seem "reasonable"? (The Bayesian estimator, an alternative one that combines one's prior beliefs about parameter values with the sample data, provides a nonzero estimate of ; it equals (Y + 1)/(N + 2) = .25 when the prior belief is that is equally likely to be anywhere between 0 and 1.)