Two basketball teams (call them d and u) are playing 3 basketball games. let θ denote the probability that u beats d in a game. if you knew θ then assume that the outcomes of the three games can be modeled as three bernoulli trials with probability of success θ (ie, the outcomes of the three games are independent with the same success probability for u namely θ which does not change over the three games). you may also assume the chance of a tie is zero. however since we don't know θ, assume p(8-1/3) 0.25, p(θ = 1/2) 0.25, p(9-2/3) = 0.5. let x denote the number of games u wins (a) | 2 points find the joint probability mass function of (θ, x) namely fill in the table 1/3 round to 4 decimal places. (b) | 2 points find the conditional pmf of θ given that u won all 3 games (c) 2 points) find e(ax = 3)