A pair of fair, six-sided dice are tossed independently of each other.
a) List the sample space of this experiment.
b) Define a random variable X to be the sum of the dice. Write down the probability mass function of X.
c) What is the probability that X is at most 4?
d) Given that X is at least 6, what is the probability that it is less than 10?
e) Define another random variable Y to be the maximum value of either die in the pair. Write down the probability mass function of Y.
f) Find the probability that Y is odd.
g) Find the expected value of Y. h) Find Var(-1.2Y + 4)