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.