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Consider a security X with date-3 payoff dened as X = d1 + d2 + 033 Let Y be the payoff to a put option on X with a strike price of K = $2.5 and maturity of T = 3. Recall that the payoff for this put option is Y = max(K X, D). (a) Describe Y as a map: Y : : 11%. (b) Is Y a random Variable of the probability space (S1,.F2,P2)? Why or why not? (c) Find the smallest possible caralgebra that makes Y a random variable