URGENT ADVANCED MATH HELP!!!

Consider theLtwo-armved bandit problem with 0/ 1 rewards where the safe arm is a Bernoulli distribution with mean (1 + 6)/2 and the risky arm is a Bernoulli distribution with mean (1 - e)/2, both distributed independently of each other and the history. Show that the maximum likelihood estimator of the safe arm given the revealed rewards is determined by the sign of 201 - 2G2 + 32 - 31 (positive sign corresponds to arm 1 and negative sign corresponds to arm 2) where G1 and 02 are the cumulative revealed rewards of arm 1 and arm 2 respectively, and .91 and 52 are the total number of times arm 1 and arm 2 respectively were previously chosen by the player. [Hint: by the independence assumptions you can write down the probability pg of observing Gl ones and 31 GI zeros from arm 1 and 02 one and .92 Gz zeros from arm 2 assuming arm i is safe as the PDFS of a binomial random variable; then consider the ratio 1221 /p2.] Note the policy that chooses the arm according to this MLE entails no exploration (greedy policy). Denote by a1 and :12 the Bernoulli random variables distributed according to the dis- tributions of arm 1 and 2 respectively. Given that in this problem (11 = 1 0.2, can you suggest a simple procedure for converting a sample of reward from arm 1 into a sample of reward from arm 2'? Can you (informally) argue that therefore no exploration is not needed in this simplied