answer all questions with explanation

Professional Magic. Your aunt (who is a professional magician), claims to have created a pair of magical coins that share a connection to each other that makes them land in the same way. The coins are always flipped at the same time. For a given flip i E {1, 2, 3...}, let Xi be a Bernoulli random variable representing the outcome of the first coin, and let Y, be a Bernoulli random variable representing the outcome of the second coin. You assume that each flip of the pair is independent of all other flips of the pair. You also assume that P(X; = 0) = P(X, = 1) = P(Y; = 0) = P(Y; = 1) = 1/2, and write, P(X; = Yi) = P. Your aunt claims that p > 1/2. You design a test to evaluate your aunt's claim. You flip the coins 3 times and define your test statistic to be the sum X1 + Y1+ X2 + Y2 + X3 + Y3 Your null hypothesis is that p =1/2. You plan to reject the null if your test statistic is 0 or 6. (a) What is the type 1 error rate of your test? (b) What is the power of your test for the alternate hypothesis that p = 3/4