Question 1 Sums of Normally Distributed Random Variables (6 Points) Consider two random variables, X, and Y. Let X be no

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Question 1 Sums Of Normally Distributed Random Variables 6 Points Consider Two Random Variables X And Y Let X Be No 1 (76.8 KiB) Viewed 19 times

Question 1 Sums of Normally Distributed Random Variables (6 Points) Consider two random variables, X, and Y. Let X be normally distributed with mean ux and variance oz. Let Y be normally distributed with mean Ủy and variance oị. Part 1.1 What is the probability that a realization x of X is less than the mean, i.e. P(x <ux)? Explain. Part 1.2 Define Z to be * X. What do you know about the distribution of Z? What is its mean? What is its standard deviation? Part 1.3 Now let us define the new random variable C=X+cY. Do you think it is possible that the variance of the new variable C is less than the variance of both X and Y? Please explain. Note: X and Y are two different random variables, so you are not allowed to say that you simply subtract X from itself and get a constant of zero.