Math Help - Exponetial distribution problem

1. Exponetial distribution problem

Can anyone help me solve this - I get negative values...

When I go swimming, the distance in meters that I can swim before getting cramp in one of my hands is exponentially distributed with mean 332.4 meters. What is the probability that, on a random occasion when I go swimming, I swim a total of at most 493.1 meters without getting hand cramp given that I swim at least 324.5 meters without getting cramp?

Thanks, F

3. Re: Exponetial distribution problem

Now i just get zero for all my probabilities:

Can you confirm that the question is asking:

P(x=493.1| 324.5<X<493.1) because to not get cramp would mean swimming the longest distance before getting it?

However, when I use these big numbers in the standard exp dist functions of:
letting lamda = 332.4, a = 324.5, b = 493.1 and z = 493.1

( exp (-lamda*z)-exp(-lamda*a) ) / ( exp (-lamda*b)-exp(-lamda*a))

Which would cancel (must mean I'm wrong somewhere). But even putting in exp(-163906) it always zeros?!?

4. Re: Exponetial distribution problem

First, $E[X]=\frac{1}{\lambda}=332.4$, so $\lambda=\frac{1}{332.4}$.

Second, exponential distribution is continuous, so the probability that $X$ equals any concrete real number is zero.

Can you confirm that the question is asking:

P(x=493.1| 324.5<X<493.1)
I think that "swim a total of at most 493.1 meters" means $X\le493.1$ and "swim at least 324.5 meters" means $X\ge324.5$. So, the question is to find $\mbox{Pr}(X\le493.1\mid X\ge324.5)=1-\mbox{Pr}(X>493.1\mid X>324.5)$. Now you can use the memorylessness property of the exponential distribution.