Let X and Y Be Two Independent Random Variables with the Following

Essay

Let X and Y be two independent random variables with the following probability distributions: $$\begin{array}{l}\begin{array} { l | r r r } x & 1 & 2 & 3 \\\hline p ( x ) & 0.2 & 0.5 & 0.3\end{array}&\begin{array} { l | r r r } y & - 1 & 0 & 1 \\\hline p ( y ) & 0.3 & 0.3 & 0.4\end{array}\end{array}$$ a. Find the probability distribution of the random variable XY.
b. Check whether E(XY) = E(X) ´ E(Y) by separately evaluating each side of the equality.