10. Let X, Y, Z be iid random variables, each with density f(u) = 2u for...

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10. Let X, Y, Z be iid random variables, each with density f(u) = 2u for 0 < u < 1 and 0 elsewhere Let M = max(X, Y, Z). That is, M(w): = max (X(w), Y (w), Z(w)) where w is any point in the probability space S. We evaluate X(w), Y (w), Z(w) for each w = S, and M(w) has the value that is the maximum of the three values. 1. a) Compute P (M 1) 2. b) Calculate the cdf of M: that is, calculate G(y) = P(M y) for y 0 3. c) Compute the density function g of M. Be sure to include where it is 0 and where it is not. 10. Let X, Y, Z be iid random variables, each with density f(u) = 2u for 0 < u < 1 and 0 elsewhere Let M = max(X, Y, Z). That is, M(w): = max (X(w), Y (w), Z(w)) where w is any point in the probability space S. We evaluate X(w), Y (w), Z(w) for each w = S, and M(w) has the value that is the maximum of the three values. 1. a) Compute P (M 1) 2. b) Calculate the cdf of M: that is, calculate G(y) = P(M y) for y 0 3. c) Compute the density function g of M. Be sure to include where it is 0 and where it is not.