1. A coin is tossed 3 times. Discrete random variable X is equal to the number of times Heads comes up. Discrete random variable Y has the value 1 if the first toss comes up heads and 0 otherwise.
(a) Find Pr[(X=1)n(y=1)]
Are X and Y independent random variables?
Solution. We can get joint cmf as follows
X 0 1 2 3
This shows how to determine if two variables are independent random variables.