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.

Question

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.

Quizplus · Accepted Answer

The Answer of 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.

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