Let X denote the number of heads obtained when a fair coin is tossed 4 times.
(a) What is E(X) and Var(X)?
(b) Repeat 10 times the experiment of tossing a fair coin 4 times and recording the number of heads obtained. You thus obtain a random sample of size 10 from a binomial distribution with 4 trials and p = 1/2. Write down the ten numbers.
(c) Based on your ten observations, estimate the mean and variance of X. Are your estimates close to the theoretical values in part (a)?