statistic HW

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

2.
Let us define another random variable 2 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 2.
b) Graph them.
c) Calculate the Expectation of Z.