# Thread: conditional expectation and variance

1. ## conditional expectation and variance

Let X, Y be independent exponential random variables with means 1 and 2 respectively.

Let
Z = 1, if X < Y
Z = 0, otherwise

Find E(X|Z) and V(X|Z).

We should first find E(X|Z=z)
E(X|Z=z) = integral (from 0 to inf) of xf(x|z).
However, how do we find f(x|z) ?

2. Originally Posted by allrighty
Let X, Y be independent exponential random variables with means 1 and 2 respectively.

Let
Z = 1, if X < Y
Z = 0, otherwise

Find E(X|Z) and V(X|Z).

We should first find E(X|Z=z)
E(X|Z=z) = integral (from 0 to inf) of xf(x|z).
However, how do we find f(x|z) ?

Bayes theorem:

$f(x|z)=\frac{p(z|x)f_X(x)}{p(z)}$

RonL