The following gambling game has been proposed, which a player must pay to play. First, a value U is chosen uniformly from the set [0, 10]. Next, a number is chosen according to a Poisson random variable with a parameter U. Letting X be the number chosen, the player receives $X. Find E[X], which is the amount a player should pay to make this a fair game HINT: Use the Law of Total Probability for Expectations, E[X]