Math Stats Problem?

[Evan]

Two fair six-sided dice are tossed independently . Let M = the maximum of the two tosses (so M(1,5) = 5, M(3,3) = 3, etc.).

a. What is the pmf of M? [Hint: first determine p(1), then p(2), and so on.]
b. Determine the cdf of M and graph it.

Note: pmf = probability mass function; cdf = cumulative distribution function.

[LuLu49]

This will be a bit of a slog
M(1,1) = 1 so P(M=1) = 1/36
M(2,2) = 2 has prob of 1/36
M(1,2) = 2 has prob of 2 x 1/36 = 2/36
P(M=2) = 3/36
etc
CDF(M=1) = 1/36
CDF(M=<2) = 1/36 + 3/36 = 4/36
etc
Make sure that CDF(M=<6) = 1 and you should be OK

[cidyah]

Here's the outcome. The rightmost number is the maximum.
1---2---2
1---3---3
1---4---4
1---5---5
1---6---6
2---3---3
2---4---4
2---5---5
2---6---6
3---4---4
3---5---5
3---6---6
4---5---5
4---6---6
5---6---6
Probability mass function of M (max) is:
m---p(m)
2-------1/15
3-------2/15
4-------3/15
5-------4/15
6-------5/15

cdf
m--------F(m)
2---------1/15
3---------3/15
4---------6/15
5---------10/15
6----------1