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 ipped at the same time. For a given ip i E {1,2,3m}, let Xi be a Bernoulli random variable representing the outcome of the rst coin, and let Y; be a Bernoulli random variable representing the outcome of the second coin. You assume that each ip of the pair is independent of all other ips of the pair. You also assume that Pa; = 0) = Pa; = 1) = as = 0) : Pm = 1) = 1/2, and write, Pun : n) : p. Your aunt claims that p > 1/2. You design a test to evaluate your aunt's claim. You ip the coins 3 times and dene your test statistic to be the SUIIle +Y1 +X2 +Y2 +X3 +Y3 Your null hypothesis is that p = 1/2. You plan to reject the null if your test statistic is O 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