Let random variables X and Y respectively denote the number of heads and tails obtained in a sequence of n independent flips of a fair coin.
(a) What kind of discrete random variable is X? Specify its range, PMF values,mean and standard deviation.
(b) Let D = X−Y denote the difference between the number of heads and tails. Usingthe central limit theorem, find a suitable approximation for the probabilitythat |D| > m, where m is a positive integer m.
(c) Evaluate this probability for the following special situation involving a very large number of flips: n = 1020 and m = 109(i.e. the difference between the number of heads and tails exceeds one billion!)
