For both parts of the problem, be careful about your rounding, e.g., 3.96 should be rounded to
4.0 . (a) Alice plays a series of card games at a casino. She declares prior to each game how
much money she bets on the game. If she wins the game, she wins as much money as she bets.
Otherwise, she loses as much money as she bets. Assume that she wins each game with
probability 0.5 , and the outcomes of the games are mutually independent. Suppose she initially
has 56 dollars, and she bets 2 dollars at each game for 25 games. Let X be the number of games
Alice wins after all the games and S be the total amount of money Alice has after all the games,
and S=aX+b. Find the values of a and b. (b) Using the Gaussian approximation with continuity
correction, express the probability Alice has more than or equal to 30 dollars left after all the
games in term of the Q function.