1. Evgeni bakes a cake and invites two friends to join him in eating it. The cake will be evenly split between whoever shows up and Evgeni. His friends know that Evgeni is an erratic baker at best, and each of them tosses a coin, independently of the other, to decide whether they will go or not. Let X be the fraction of the cake that Evgeni gets to eat. For example if 1 friend shows up, Evgeni gets half the cake, if 2 show up, he gets one-third of the cake. Write down the PMF of X. Does X have one of the named distributions (Bernoulli, Binomial, Discrete uniform)? If so, what are its parameters? What is the probability that Evgeni gets at most half the cake?