How do you simulate an exponential random variable over an interval $[0, T]$ with $T > 0$?

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    $\begingroup$ Do you know mathematics stack exchange ? $\endgroup$ – MJ73550 Dec 17 '16 at 21:24

You should post on mathematics.stackexchange

I answer but I should not.

Let $X $ be an exponential r.v. of parameter $\lambda $ $$P (X<u|X <T)=\frac {P (X<min (u,T))}{P (X <T )} $$ So for $0\leq u\leq T$ $$P (X<u|X <T)=\frac {1-\exp (-\lambda u)}{1-\exp (-\lambda T)} $$

So if $U $ is an uniform on $ [0,1]$ then $$Y= -\frac {1}{\lambda }\ln\left (1-U (1-\exp(-\lambda T))\right) $$ is an exponential r.v. of parameter $\lambda $ conditionned to be on $[0,T] $


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