ASM 47.8 v8

[DrNO811]

I'm trying to solve this problem by calculating the probability of each outcome, and finding the expected value based on that, but I'm messing up my probabilities.

I get the possible values as 2, 4, 5, 7, and 10. I get their respective probabilities as (1/3), (1/9), (1/9), (5/18), and (1/9). I realize these don't sum to 1, and that's my problem...I've double checked everything and not found the mistake. Does anyone know what the correct probabilities should be?

[rekrap]

Bayes?

Take each probability over the sum of all probabilities.

[Kenny]

It looks like he is trying to calculate the prior probabilities, which should sum to 1.

[pcact]

E(X) = 2*2/3 + 5*1/3 = 3
E(Y) = 2*1/3 + 5*2/3 = 4

E(S|A) = 2/3 * 3 + 1/3 * (4*2/9 + 7*5/9 + 10*2/9) = 13/3
E(S|B) = 1/3 * 3 + 2/3 * 7 = 17/3

E(S) = 1/2 * 13/3 + 1/2 * 17/3 = 30/6 = 5

[DrNO811]

Exactly, Kenny. 47.8 is just asking for the prior expected value. My prior probabilities are off, but I keep looking over it, and can't find the mistake.

[DrNO811]

pc, thanks for posting that, but that basically just shows me the same thing as the solution. I was trying to approach it slightly differently, by calculating the probability of each outcome, and it isn't working.

[DrNO811]

found it...gosh I hate bayesian credibility...so many simple calculations...it's just so easy to make a stupid mistake.

[Kenny]

Pr(X=2) = 0.5(2/3^2 + 1/3*2/3) = 1/3
Pr(X=4) = 0.5(1/3*2/3*1/3 + 2/3*2/3*1/3) = 1/9
Pr(X=5) = 0.5(2/3*1/3*2) = 2/9
Pr(X=7) = 0.5(1/3*(2/3^2 + 1/3^2) + 2/3(2/3^2 + 1/3^2)) = 5/18
Pr(X=10) = 0.5(1/3*(1/3*2/3) + 2/3*(1/3*2/3)) = 1/9

ok, where is my math mistake? This is why doing the problem like this is dumb!

[pcact]

I get the possible values as 2, 4, 5, 7, and 10. I get their respective probabilities as (1/3), (1/9), (1/9), (5/18), and (1/9).

2: 1/2 * 2/3 * 2/3 + 1/2 * 1/3 * 2/3 = 1/3
4: 1/2 * 1/3 * 2/9 + 1/2 * 2/3 * 2/9 = 1/9
5: 1/2 * 2/3 * 1/3 + 1/2 * 1/3 * 1/3 = 1/6
7: 1/2 * 1/3 * 5/9 + 1/2 * 2/3 * 5/9 = 5/18
10: 1/2 * 1/3 * 1/3 * 2/3 + 1/2 * 2/3 * 1/3 * 2/3 = 1/9

1/3 + 1/9 + 1/6 + 5/18 + 1/9 = 1

[Kenny]

found it, thanks pcact.