u v" n... Let X and Y be independent random variables, where o X is uniform on [0, 1]. and 0 Y is a standard normal random variable. (a) (2 points) Write down Var(X) and Var(Y). You don't need to justify your answer. (b) (2 points) Find Var(6X Y). (c) (3 points) Find the correlation Corr(6X Y, 21'). Q Please select file(s) Select file(s] 07 Problem 5 (long answer) 6 Points Your parents have two kittens, Wes and Jess. You take one of the kittens to your house for a day but you don't know which one it is, so you assume that the probability of the cat being Wes is 1/2 and the probability of the cat being Jess is 1/2. You know that the number of times that Wes meows in a day is a Poisson random variable with mean 10, and the number of times that Jess meows in a day is a Poisson random variable with mean 20. (a) (2 points) What is the probability that the kitten meows exactly 15 times given that the kitten is Jess? (b) (4 points) What is the probability that the kitten you have is Jess given that the kitten meows exactly 15 times