Answer:
12.25
Step-by-step explanation:
There are 36 outcomes in a throw of 2 dice throws here.
The amount we would be willing to pay is computed here as the expected product value for the 2 dice as we are risk neutral, therefore we would be using the expected value.
The expected values here are computed as:
X P(X = x) xP(X =x)
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
36 441
Using the above table, the expected amount here is computed as:
[tex]E(X) = \frac{441}{36} = 12.25 [/tex]
Therefore 49/4 is the required expected value here.
The expected value represents the amount you are willing to pay.
The amount you are willing to pay is #12.25
Let the dice be A and B.
So, we have:
[tex]A = \{1,2,3,4,5,6\}[/tex]
[tex]B = \{1,2,3,4,5,6\}[/tex]
The sample space of the product of the outcomes of the dice is:
[tex]S = \{1,2,3,4,5,6\\2,4,6,8,10,12\\3,6,9,12,15,18\\4,8,12,16,20,24\\5,10,15,20,25,30\\6,12,18,24,30,36\}[/tex]
The sample size is:
[tex]n(S) = 36[/tex]
The amount you are willing to pay is the expected value of the sample space.
This is calculated using:
[tex]Expected = \frac{\sum(S)}{n(S)}[/tex]
[tex]Expected = \frac{1+2+3+4+5+6+.......+36}{36}[/tex]
[tex]Expected = \frac{441}{36}[/tex]
[tex]Expected = 12.25[/tex]
Hence, the amount you are willing to pay is #12.25
Read more about expected values at
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