Each throw of a 6-sided die lands on each of the even numbers 2,4,6 with probability c and on each one of the odd numbers 1,3,5 with probability 2c.

a) Find c. Suppose the die is tossed. We introduce two random variables X and Y . Let X equal 1 if the result is greater than 3 and 0 otherwise. Let Y equal 1 if the result is odd and 0 otherwise.
b) Find the joint probability mass function of X and Y .
c) Are the random variables X and Y independent? Justify your answer.
d) Compute ErX2 ? Y s.