I throw two dice. The random variable X gives the result of the first die and the random variable Y gives the result of the sum of the two dice. What is the value of E(Y!X)?
Asked
Active
Viewed 82 times
0
-
What does $Y!X$ mean? – Emanuele Paolini Jan 01 '14 at 22:10
-
@EmanuelePaolini: I was assuming it meant conditional expectation as in $E[Y|X]$. – copper.hat Jan 01 '14 at 22:26
-
But don't you need an event on the right hand side of $|$? – Emanuele Paolini Jan 01 '14 at 22:29
-
@EmanuelePaolini: It is conditioned by the $\sigma$-field generated by $X$ as in http://en.wikipedia.org/wiki/Conditional_expectation#Formal_definition – copper.hat Jan 01 '14 at 22:37
1 Answers
2
Let $D_1,D_2$ be the value of each throw. Assume the throws are fair and independent.
Then $E[D_1+D_2|D_1] = E[D_1|D_1]+E[D_2|D_1] = D_1+E[D_2] = D_1+{7 \over 2}$.
In terms of the question variables, $E[Y|X] = X+ {7 \over 2} $.
copper.hat
- 172,524