Two fair sixsided dice are tossed independently Let M the m

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.] (Enter your answers as fractions.)

(b) Determine the cdf of M. (Enter your answers as fractions.)

F(m) =

Graph the cdf of M.

Solution

a)

P(1) = P(M=1) = P(1,1) = 1/36

P(2) = P(m=2) = P[(1,2)or (2,1) or (2,2)] = 3/36

P(3) = P(M=3) = P [(1,3) or (2,3) or (3,1) or (3,2),(3,3)] = 5/36

similarly
p(4) = 7/36

p(5) = 9/36

p(6) = 11/36

b)

CDF is

0    for m<1

1/36 for 1<=m <=2

4/36 for 2<= m <=3

9/36 for 3 <= m <= 4

16/36 for 4 <= m <=5

25/36 for 5 <= m <= 6

1      for m>=6

c)

graph of the cdf is 4th graph