3. Let Z ~ N(0, 1) and define Y = max{ Z, 0}. In other words, if Z is positive then Y = Z, and if Z is negative then Y = 0. (a) What is P(Y = 0)? (b) Explain why Y is neither a discrete nor continuous random variable. (c) Let F(x) be the CDF of Y. Write a formula for F(x) in terms of &, the standard Normal CDF, and draw the graph of F(x). Hint: Try plugging in various x-values into F. Determine the value of F(x) by figuring out which values of Z would lead to Y being less than or equal to x