Thank you for your help

We all know that casinos have a slightly better odd at getting your money. Suppose you play the following game and they use an unfair coin, which has a probability of 1/2 + e to yield a head (H ) Otherwise, a tail (T) is yielded. Here, 6 is small but positive real number. You lose a dollar when H (X = 1) shows up and gain a dollar when T (X = 1) shows up. [5 pts] (A) Compute the generating function wN(k:) for your expected gain per one coin- tossing 5N = (1 /N ) 2.13:1 X3- (X5 = :l:1). Recall that the generating function is dened as WNUV) E km\")- (1) [3 pts] (B) 00mpute the mean and the variance of SN. [7 pts] (C) Using the generatiOn functiOn, nd the density distribution function fN for the uctuation of 3N and explain how your answers demonstrate the law of large numbers and the central limit theorem