Thread: conditional probability

The definition of the conditional probability f(x|y)=f(x,y)/f(y)
but what is now f(x|x>a), because I don't know what f(x,x) is.
And what is E(X|X>a) for a random variable X then

thx

Originally Posted by sung

The definition of the conditional probability f(x|y)=f(x,y)/f(y)
but what is now f(x|x>a), because I don't know what f(x,x) is.
And what is E(X|X>a) for a random variable X then

thx

$\displaystyle f(x|x>a)=f(x)/Pr(x>a)$, when $\displaystyle x>a$ and zero otherwise, and $\displaystyle Pr(x>a)=1-F(a)$

$\displaystyle E(X|X>a)=\int_a^{\infty} x f(x|x>a)\; dx$

CB