Suppose that n takes the values 0 1 2 3 with probabilities, Ask an Expert

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Suppose that N takes the values 0, 1, 2, 3 with probabilities 0.4, 0.3, 0.2, 0.1 respectively, and that X takes the values 10 with a probability of 0.5, 20 with a probability of 0.3, 30 with a probability of 0.1, and various other values, all higher than 30, with a total probability of 0.1. (You are not given these values.)

(a) Find the probability that S = 30.

(b) Find E[(S - 15)+], given that E(X) = 20.

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