Question 2 Let o and @ be the pdf and cdf, respectively, of the standard normal variable Z. Let X = 2Z - 3. Let Y be a binomial random variable, independent of X, with parameters n = 10 and p = 0.2. (a) Can you determine P(X = 1[Y = 2)? If so, calculate this probability. (5 marks) (b) Determine the probability for which X is within one standard deviation of its mean. (5 marks) (c) Appraise if we may determine the mean, median and variance of R = X + Y. If so, compute them. (10 marks) (d) Let Z1, Z2, .., Z5 be 5 independent standard normal random variables. For each j = 1, ...,5, define Xj = 2Z; - 3 Let s -4[(x + 3) Using what you understand about normal random variables and the random variables associated with it, describe how you would compute P(S > 2). Therefore, compute P(Y > 2 5 > 2). (10 marks)