SOLUTION: Let a fair die be rolled n times. Let’s make an assumption that all rolls of a die are independent. If x and y are the outcomes of any two of n trials, what is the distribution

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Question 540961: Let a fair die be rolled n times. Let’s make an assumption that all rolls of a die are independent. If x and y are the outcomes of any two of n trials, what is the distribution function of XY?

Answer by AnlytcPhil(1807) About Me  (Show Source):
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Let a fair die be rolled n times. Let’s make an assumption that all rolls of a die are independent. If x and y are the outcomes of any two of n trials, what is the distribution function of XY 
1×1=1  1×2=2  1×3=3  1×4=4  1×5=5  1×6=6

2×1=2  2×2=4  2×3=6  2×4=8  2×5=10 2×6=12

3×1=3  3×2=6  3×3=9  3×4=12 3×5=15 3×6=18

4×1=4  4×2=8  4×3=12 4×4=16 4×5=20 4×6=24

5×1=5  5×2=10 5×3=15 5×4=20 5×5=25 5×6=30

6×1=6  6×2=12 6×3=18 6×4=24 6×5=30 6×6=36

The products are 1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,30,36

XY   no. of ways   P(xy)
 1       1         1/36
 2       2         2/36
 3       2         2/36
 4       3         3/36
 5       2         2/36
 6       4         4/36
 8       2         2/36
 9       1         1/36
10       2         2/36
12       4         4/36
15       2         2/36
16       1         1/36
18       2         2/36
20       2         2/36
24       2         2/36
25       1         1/36
30       2         2/36
36       1         1/36


Edwin