Question: 2018 Winter Final - 21
You are given two independent random variables $X$ and $Y$, where
Define the random variable $Z = X \cdot Y$. Which of the following is correct?
| $\Pr(X = 0)$ | $= \Pr(X = 1) = \Pr(Y = 0)$ $= \Pr(Y = 1) = 1/2.$ |
(a)
The random variables $X$ and $Z$ are independent.
(b)
All of the above.
(c)
None of the above.
(d)
The random variables $X$ and $Z$ are not independent.