2. Suppose that X and Y are independent random variables, both with the standard normal distribution i.e. X, Y~ N(0, 1). For pe [-1, 1], define √1-p²X + pY. Show that E[ZY] = pY. Z:=

c) The random variable X is normally distributed such that X~N(µ, 12). It is known that P(X > 32) = 0.0618. find the value of μ.

A random sample X1, X2, ..., Xn is obtained for a random variable X believed to be distributed as Beta(a, 7) (notice that B = 7 is known). Use the method of moments to determine the value of given 0.72.

Suppose that Yis a continuous random variable, with Y ~ Normal(µ, o²) where the two parameters and take values 2 and 0.5 respectively. Using the table of the Normal distribution, compute P(Y > y) if y=1.608. Give your answer to 3 decimal places. Note that the Normal table can be used for arguments specified up to two decimal places, so round your arguments appropriately.