I need to find $E[x\mid x>1]$ if $X \sim \exp(\lambda)$.
I first tried: $f(x|x>1) = \frac{f(x)}{\int_{x=1}^{\infty}f(x) dx}.$
I need to find $E[x\mid x>1]$ if $X \sim \exp(\lambda)$.
I first tried: $f(x|x>1) = \frac{f(x)}{\int_{x=1}^{\infty}f(x) dx}.$
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.