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Two fair dice are tossed together. Let X be the sum and Y the product of...

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Statistics

Two fair dice are tossed together. Let X be the sum and Y theproduct of the two numbers on the top of the dice. Calculate E(X+3Y).

Answer & Explanation Solved by verified expert
4.3 Ratings (596 Votes)

If two dice are tossed the possible outcomes are 1,2,3,4,5,6 on each die. To obtain sum and product.

Dice 1 Dice 2 X (sum ) Y (product)
1 1 2 1
1 2 3 2
1 3 4 3
1 4 5 4
1 5 6 5
1 6 7 6
2 1 3 2
2 2 4 4
2 3 5 6
2 4 6 8
2 5 7 10
2 6 8 12
3 1 4 3
3 2 5 6
3 3 6 9
3 4 7 12
3 5 8 15
3 6 9 18
4 1 5 4
4 2 6 8
4 3 7 12
4 4 8 16
4 5 9 20
4 6 10 24
5 1 6 5
5 2 7 10
5 3 8 15
5 4 9 20
5 5 10 25
5 6 11 30
6 1 7 6
6 2 8 12
6 3 9 18
6 4 10 24
6 5 11 30
6 6 12 36

table for X

X value (x) Frequency (f) x*f
2 1 2
3 2 6
4 3 12
5 4 20
6 5 30
7 6 42
8 5 40
9 4 36
10 3 30
11 2 22
12 1 12
Total 36 252

E(x) = sum(f*x)/sum(f) = 252/36 = 7

table for Y

Y value (y) Frequency (f) f*y
1 1 1
2 2 4
3 2 6
4 3 12
5 2 10
6 4 24
8 2 16
9 1 9
10 2 20
12 4 48
15 2 30
16 1 16
18 2 36
20 2 40
24 2 48
25 1 25
30 2 60
36 1 36
Total 36 441

E(y) = sum(f*y)/sum(f) = 441/36 = 12.25

E(X+ 3Y) = E(X) + 3*E(Y) = 7 + 12.25*3 = 7 + 36.75 = 43.75
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