2. Two fair six-sided dice are tossed independently. Let M = the maximum of the two…
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Question “2. Two fair six-sided dice are tossed independently. Let M = the maximum of the two…”
2. 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) I4 ptsl Find the probability mass function of M. (b) 14 pts] Find the cumulative distribution function of M and graph it. (c) 12 pts] Find the expected value of M (d) 12 pts] Find the variance of M. (e) 12 pts] Find the standard deviation of M.
Answer
Solution:
we are given that : two fair six sided dice are
tossed independently.
M = Maximum of the two tosses.
Thus we get:
First Die
Second Die
M = Maximum of two dice
1
1
1
1
2
2
1
3
3
1
4
4
1
5
5
1
6
6
2
1
2
2
2
2
2
3
3
2
4
4
2
5
5
2
6
6
3
1
3
3
2
3
3
3
3
3
4
4
3
5
5
3
6
6
4
1
4
4
2
4
4
3
4
4
4
4
4
5
5
4
6
6
5
1
5
5
2
5
5
3
5
5
4
5
5
5
5
5
6
6
6
1
6
6
2
6
6
3
6
6
4
6
6
5
6
6
6
6
Part a) Probability mass function of M.
We need to find frequencies of each possible values of M and
then divide each frequency by N = 36
M
f = frequency
P(M)
1
1
0.0278
2
3
0.0833
3
5
0.1389
4
7
0.1944
5
9
0.2500
6
11
0.3056
N = 36
Part b) Cumulative distribution function of M and Graph
it.
To get cumulative distribution function , we need to find F(M)
column
That is find cumulative sum of probabilities of each value of
M.
Above is the solution for “2. Two fair six-sided dice are tossed independently. Let M = the maximum of the two…“. We hope that you find a good answer and gain the knowledge about this topic of math.
