Problem 29SE

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.

Step 1 of 5:

The experiment here is tossing a penny and nickel.

Let X denotes the outcomes when a penny is tossed and let Y denotes the outcomes when a nickel is tossed.

If X=1,then the outcome is head and if X=0 then the outcome is tail for a penny.

If Y=1,then the outcome is head and if Y=0 then the outcome is tail for a nickel.

It is also given that,

0.4,=0.6 and

=0.6,=0.4