a. Realizing that the most probable outcome from a series of N coin tosses is N/2 heads and N/2 tails, what is the expression for W_maxcorresponding to this outcome?

b. Given your answer for part (a), derive the following relationship between the weight for an outcome other than the most probable and W_max:

c. We can define the deviation of a given outcome from the most probable outcome using a €œdeviation index,€ α = H €“ T / N. Show that the number of heads or tails can be expressed as H = N / 2 (1 + α) and T = N / 2 (1 €“ α).

d. Finally, demonstrate that

N! %3! agla7! = -Hlog N/2 log T log N/2