Select true statements

Allie and Michelle like to gamble. In any round of the betting game they play, a bet by Allie or Michelle is equally likely to return triple the bet or return zero, independent of any other bet placed. Allie starts with 100 dollars and in each round she bets all of her money. Thus, after the first round, Allie will have A1 = 100Y1 dollars where Y1 has PMF 1/2 y = 0, Py (y) = 1/2 y = 3, 0 otherwise After n rounds, Allie will have An = 100Y,Y2 . . . Yn dollars where Y1, . . ., Yn are iid random variables. Michelle also starts with 100 dollars but she is a more cautious gambler; in each betting round, Michelle bets exactly ten percent of her money. After the first round, Michelle will have M1 = 100(0.9 + 0.1Y1 ) dollars. After n rounds of betting, Michelle will have My dollars. Michelle's friend Lydia tells Michelle she should compute her logarithmic return using In = In(Mn). Select the true statements from the following ten statements: After n rounds, E[Ln] = In(100) + (0.0385)n. After 8 rounds, the probability that Allie has zero money is P [A2 = 0] = 255 /256. After 1 round, E [L1] = 4.6437. Using a Central Limit Theorem approximation, after 36 rounds, P[M36 > 200] = Phi(0.802) ~ 0.7887. After n rounds, the probability that Allie is broke is P[An = 0] = 1 - (1/2)". After 1 round, the expected amount of money Allie will have is E[Al] = 150 dollars. After n rounds, E[Mn] = 100(1.1)". After n rounds, In = In(100) + Wn where Wn is a sum of n iid random variables. O After n rounds, In has variance var[In] = (0.0385)n. V After 1 round, the expected amount of money Michelle will have is E[M] ] = 100.5 dollars