1.

Let us define a random variable Y as the sum of number of dots from tossing two fair dice. For example, if we roll a 2 and a 3, then Y=5.

a) Tabulate the probability distribution and cumulative distribution of Y.

b) Graph them. c) Calculate the Expectation of Y.

(Hints: you should enumerate all the possible outcomes of tossing two dice, shown below, in order to 1) identify the set of values that Y can take on and 2) figure out the probability associated with each value.)

number rolled from the second die
number rolled from the first die	1	2	3	4	5	6
1
2
3
4
5
6

2.

Let us define another random variable Z as the higher number of dots of the two dice. For example, if we roll a 2 and 3, then Z=3; if we roll 2 and 6, then Z=6; if we roll 5 and 5, then Z=5.

a) Tabulate the probability distribution and cumulative distribution for Z.

b) Graph them. c) Calculate the Expectation of Z.