[Random Variables, Normal distribution] [From the final exam, 2023, Fall semester] Suppose X is a standard normal random variable, so X ~N(0, 1). Let Y is another random variable that is defined as Y: So, if x < 1.96; = 1, if X 1.96. (a) What is the type of random variable Y (discrete or continuous) and how is the corresponding distribution called? What is the support of Y? (b) Obtain the probability mass function for Y. (c) Compute E(Y) and V(Y). (d) Are X and Y independent random variables? Explain your answer. (Hint: formal analysis is not expected here, only provide the intuition)