2. A coin with heads probability p is tossed repeatedly and independently. Let Hr. and T\" be the number of times heads and tails appear, respectively, in the rst it tosses Find: (a) E[H,,], (b) Var(Hn), (c) Var(Hn + Tn). Represent the parity of H\" by the random variable Zn that is 0 if H" is even and 1 if H\" is odd. For example, if H5 = 4 then Z5 = 0, while if H5 = 3 then Z5 = l. (d) For 12 = 1/2, nd P(Z,, = l) for all n. (e) For which values of 0 S p g 1 are Zn and Zn.\" independent of each other for all n