One distribution for the occurrence of rain (because there are days with no rain) and another distribution for the amount of
precipitation. The distribution for the daily amount of precipitation is chosen to be asymmetric because usually there are more days with small precipitation quantities. Suppose that the occurrence of rain in Vancouver follows a Bernoulli distribution with probability p = 0.6. And if it rains, the daily amount of precipitation follows an exponential distribution with mean 2 millimeters. Denote the daily amount of precipitation in Vancouver by the random variable X, and the occurrence of rain by the random variable of Y .
a) Derive the cumulative distribution function of X.
b) Compute the expectation of X.
c) Compute E(Var(X|Y)).
d)Compute the variance of X.
Please show work. Thank you.