# Thread: exponential distrubtion

1. ## exponential distrubtion

I have no idea about this, i hope that someone can help me.
If the number of minutes that a doctor spends with a patient is a random variable having an exponential distrubtion with the a=9, what are the probabilities that it will take the doctor at least 20 minutes to treat one patient?

2. Hello,
Originally Posted by yuan.69
I have no idea about this, i hope that someone can help me.
If the number of minutes that a doctor spends with a patient is a random variable having an exponential distrubtion with the a=9, what are the probabilities that it will take the doctor at least 20 minutes to treat one patient?
Let X be the random variable representing the time the doctor spends with a patient.

You are looking for $P(X \geqslant 20)$
This is $1-P(X < 20)=1-P(X \leqslant 20)$

But you surely know the cumulative distribution function of the exponential distribution, don't you ?
$P(X \leqslant x)=F(x)=1-e^{-\lambda x}$, for positive x.