Mostly need help on number 3. I tried number 2 and got 12 1/4 as expected value, 6 most likely outcome 1/2 probability
thanks
2.
Greatest value = 36 Least value = 1
Possible Products
1 2 3 4 5 6
1 1 2 3 4 5 6
2 2 4 6 8 10 12
3 3 6 9 12 15 18
4 4 8 12 16 20 24
5 5 10 15 20 25 30
6 6 12 18 24 30 36
Expected value =
1(1/36) + 2(2/36) + 3(2/36) + 4 (3/36) + 5 (2/36) + 6(4/36) + 8(2/36) + 9(1/36) + 10(2/36) + 12(4/36) +
15(2/36) + 16(1/36) + 18(2/36) + 20(2/36) + 24(2/36) + 25(1/36) + 30(2/36) + 36(1/36) =
[ 1 + 4 + 6 + 12 + 10 + 24 + 16 + 9 + 20 + 48 + 30 + 16 + 36 + 40 + 48 + 25 + 60 + 36 ]
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36
441 / 36 =
12.25
3.....We can use the same product table with a modification
1 2 3 4 5 6
1 -2 2 3 4 5 6
2 2 -8 6 8 10 12
3 3 6 -18 12 15 18
4 4 8 12 -32 20 24
5 5 10 15 20 -50 30
6 6 12 18 24 30 -36
Expected value =
-2(1/36) - 8(1/36) - 18(1/36) - 32(1/36) - 50(1/36) - (36)(1/36) + 2(2/36) + 3(2/36) + 4 (2/36) + 5(2/36) +
6(4/36) + 8(2/36) + 10(2/36) + 12(4/36) + 15(2/36) + 18(2/36) + 20(2/36) + 24(2/36) + 30(2/36) =
[ -2 - 8 - 18 -32 - 50 - 36 + 4 + 6 + 8 + 10 + 24 + 16 + 20 + 48 + 30 + 36 + 40 + 48 + 60 ]
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36
204
___ =
36
17/3 ≈ 5.66