Let $X$ and $Y$ be two random variables with means and and variances and respectively. Consider the random variable $W$ that is a weighted average of $X$ and $Y$:


where $a =$. Answer the following, rounding your answers to two decimal places.

(a) What is the mean of $W$ ?

(b) Assume that $X$ and $Y$ are independent. What is the variance of $W$?

(c) Now assume that $Cov(X, Y ) =$. What is the variance of $W$?