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What is $E(X\mid X>c)$ in terms of $P(X>c)$?

I've seen conditional probability/expectation before with respect to another random variable but not to the variable itself. How would I go about interpreting this?

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    As a simple example, suppose $X$ is a discrete random variable taking on values $0$, $1$, $2$ with equal probability $\frac{1}{3}$. Then, _conditioned_ on $X > 0$, $X$ can take on values $1$ or $2$ with probability $$P\{X = i\mid X > 0\} = \frac{P(\{X = i\}\cap \{X > 0\})}{P\{X > 0\}} = \frac{P\{X = i\}}{P\{X > 0\}} = \frac{1/3}{2/3} = \frac{1}{2}, i = 1, 2$$ and so $$E[X\mid X > 0]= \frac{1}{2}\times[1 + 2] = \frac{3}{2}$$.2011-12-08

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