using the probability distribution table for the possible outcomes of rolling 2 number cubes and finding the product, find the expected value

Question

x 0 1 2 3 4 5 6 7 8 9

p(x) 0 1/18 1/12 1/6 1/36 1/36 1/18 0 1/36 1/36

.... 10 11 12 13 14 15 16 17 18

1/12 0 1/36 0 0 1/36 1/18 0 1/36

Answer 1

Expected value is a weighted average mean. It is the ∑xp(x)

So multiply each x by its probability and sum the products.

x. p(x). xp(x)

0. 0. 0

1. 1/18. 1/18

2 1/12. 1/6

3. 1/6 1/2

4. 1/36. 1/9

5. 1/36. 5/36

6. 1/18. 1/3

7. 0. 0

8 1/36. 2/9

9. 1/36. 1/4

10. 1/12. 5/6

11. 0. 0

12. 1/36. 1/3

13 0. 0

14. 0. 0

15 1/36 5/12

16. 1/18. 8/9

17. 0. 0

18. 1/36. 1/2

4.75

The expected value of these possible outcomes is 4.75.