1
$\begingroup$

I need to find $E[x\mid x>1]$ if $X \sim \exp(\lambda)$.

I first tried: $f(x|x>1) = \frac{f(x)}{\int_{x=1}^{\infty}f(x) dx}.$

  • 0
    If the expectation of the original was $1/\lambda$, then the expectation of the truncated is $1/\lambda + 1 $. This happens to the exponential, only, because of the property mentioned in André Nicolas' answer.2012-06-19

1 Answers 1

5

Hint: Use the memorylessness property of the exponential distribution. Given that you have waited $1$ hour, what is the distribution of your additional waiting time? So what is the expectation of your additional waiting time? Now don't forget to add the hour already spent waiting.

  • 0
    @ravenea: If the *parameter* in the usual sense is $\lambda$, as in density $\lambda e^{-\lambda x}$, then $\lambda/2$ is utterly impossible. It does not even have the right units, the unit for $\lambda$ is $t^{-1}$ (inverse of time).2012-06-19