The payoff (X) (in USD) for a game of lottery has the following probability distribution. X = payoff Probability 0 0.25 10 0.30 25. a 50. a 75. 0.10 100 0.05 where 0 < a < 1 is a real number. Find a and compute the expected payoff. The expected payoff is equal to: a) 10.75 USD b) 15.25 USD c) 26.75 USD d) 25.25 USD e) It cannot be estimated with the information provided