Problem 4.6 (20 points): Statistical Properties of RV
Let X be a random variable with probability density function.
$$f_x(x) = \begin{cases}
\frac{x^2}{4}, & 1<x<2 \\
0, & else
\end{cases}$$
a) What is the Expectation of the random variable Y= 3X + 3? (Hint: Y is a function. So, use the
properties of Expectation.)
b) What is the mean-square value of the random variable Y = 3X + 3?
c) What is the variance of the random variable Y = 3X + 3?
Hint: Use mean or variance properties where necessary and simplify before integrating, if any.