A penny and a nickel are tossed. The penny has probability 0.4 of coming up heads, and

Question:

A penny and a nickel are tossed. The penny has probability 0.4 of coming up heads, and the nickel has probability 0.6 of coming up heads. Let X = 1 if the penny comes up heads, and let X = 0 if the penny comes up tails. Let Y = 1 if the nickel comes up heads, and let Y = 0 if the nickel comes up tails.
a. Find the probability mass function of X.
b. Find the probability mass function of Y.
c. Is it reasonable to assume that X and Y are independent? Why?
d. Find the joint probability mass function of X and Y.