SOLUTION: please help me solve the following question �A fair die is thrown at random three independent times. Let Y be the maximum of these three outcomes, each outcome being the number

Question 998529: please help me solve the following question
�A fair die is thrown at random three independent times. Let Y be the maximum of these three outcomes, each outcome being the number shown on the face uppermost on the die. Find the probability density function of Y�.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
I used EXCEL to generate all possible outcomes and sums.
1 1 1 3
1 1 2 4
1 1 3 5
1 1 4 6
1 1 5 7
1 1 6 8
1 2 1 4
1 2 2 5
1 2 3 6
1 2 4 7
1 2 5 8
1 2 6 9
1 3 1 5
1 3 2 6
1 3 3 7
1 3 4 8
1 3 5 9
1 3 6 10
1 4 1 6
1 4 2 7
1 4 3 8
1 4 4 9
1 4 5 10
1 4 6 11
1 5 1 7
1 5 2 8
1 5 3 9
1 5 4 10
1 5 5 11
1 5 6 12
1 6 1 8
1 6 2 9
1 6 3 10
1 6 4 11
1 6 5 12
1 6 6 13
2 1 1 4
2 1 2 5
2 1 3 6
2 1 4 7
2 1 5 8
2 1 6 9
2 2 1 5
2 2 2 6
2 2 3 7
2 2 4 8
2 2 5 9
2 2 6 10
2 3 1 6
2 3 2 7
2 3 3 8
2 3 4 9
2 3 5 10
2 3 6 11
2 4 1 7
2 4 2 8
2 4 3 9
2 4 4 10
2 4 5 11
2 4 6 12
2 5 1 8
2 5 2 9
2 5 3 10
2 5 4 11
2 5 5 12
2 5 6 13
2 6 1 9
2 6 2 10
2 6 3 11
2 6 4 12
2 6 5 13
2 6 6 14
3 1 1 5
3 1 2 6
3 1 3 7
3 1 4 8
3 1 5 9
3 1 6 10
3 2 1 6
3 2 2 7
3 2 3 8
3 2 4 9
3 2 5 10
3 2 6 11
3 3 1 7
3 3 2 8
3 3 3 9
3 3 4 10
3 3 5 11
3 3 6 12
3 4 1 8
3 4 2 9
3 4 3 10
3 4 4 11
3 4 5 12
3 4 6 13
3 5 1 9
3 5 2 10
3 5 3 11
3 5 4 12
3 5 5 13
3 5 6 14
3 6 1 10
3 6 2 11
3 6 3 12
3 6 4 13
3 6 5 14
3 6 6 15
4 1 1 6
4 1 2 7
4 1 3 8
4 1 4 9
4 1 5 10
4 1 6 11
4 2 1 7
4 2 2 8
4 2 3 9
4 2 4 10
4 2 5 11
4 2 6 12
4 3 1 8
4 3 2 9
4 3 3 10
4 3 4 11
4 3 5 12
4 3 6 13
4 4 1 9
4 4 2 10
4 4 3 11
4 4 4 12
4 4 5 13
4 4 6 14
4 5 1 10
4 5 2 11
4 5 3 12
4 5 4 13
4 5 5 14
4 5 6 15
4 6 1 11
4 6 2 12
4 6 3 13
4 6 4 14
4 6 5 15
4 6 6 16
5 1 1 7
5 1 2 8
5 1 3 9
5 1 4 10
5 1 5 11
5 1 6 12
5 2 1 8
5 2 2 9
5 2 3 10
5 2 4 11
5 2 5 12
5 2 6 13
5 3 1 9
5 3 2 10
5 3 3 11
5 3 4 12
5 3 5 13
5 3 6 14
5 4 1 10
5 4 2 11
5 4 3 12
5 4 4 13
5 4 5 14
5 4 6 15
5 5 1 11
5 5 2 12
5 5 3 13
5 5 4 14
5 5 5 15
5 5 6 16
5 6 1 12
5 6 2 13
5 6 3 14
5 6 4 15
5 6 5 16
5 6 6 17
6 1 1 8
6 1 2 9
6 1 3 10
6 1 4 11
6 1 5 12
6 1 6 13
6 2 1 9
6 2 2 10
6 2 3 11
6 2 4 12
6 2 5 13
6 2 6 14
6 3 1 10
6 3 2 11
6 3 3 12
6 3 4 13
6 3 5 14
6 3 6 15
6 4 1 11
6 4 2 12
6 4 3 13
6 4 4 14
6 4 5 15
6 4 6 16
6 5 1 12
6 5 2 13
6 5 3 14
6 5 4 15
6 5 5 16
6 5 6 17
6 6 1 13
6 6 2 14
6 6 3 15
6 6 4 16
6 6 5 17
6 6 6 18
So then adding up the possible outcomes from 3 to 18.
3 1
4 3
5 6
6 10
7 15
8 21
9 25
10 27
11 27
12 25
13 21
14 15
15 10
16 6
17 3
18 1
and then dividing the outcomes by the total number of outcomes,
3 0.0046
4 0.0139
5 0.0278
6 0.0463
7 0.0694
8 0.0972
9 0.1157
10 0.1250
11 0.1250
12 0.1157
13 0.0972
14 0.0694
15 0.0463
16 0.0278
17 0.0139
18 0.0046

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