# Math Help - Exponential distributions

1. ## Exponential distributions

let X have an exponential pfd with B=500. so f(x)=(1/500)exp(-x/500) with x from 0 to infinity.
a. compute P(X>500)
b. compute the conditional probability

again thanks!

2. Originally Posted by Dubulus
let X have an exponential pfd with B=500. so f(x)=(1/500)exp(-x/500) with x from 0 to infinity.
a. compute P(X>500)
b. compute the conditional probability

again thanks!
a. This is the application of a basic definition you should be familiar with:

$\Pr(X > 500) = \int_{500}^{+\infty} \frac{1}{500} \, e^{-x/500} \, dx$.

Do the integration. Get the answer.

b. The question is incomplete. What's the given event??

3. a. thats what my book says, but somehow i remember a way of figuring this out without doing an integral...
b. thats exactly what i thought, unfortunately it says nothing further than that. any ideas what it could possibly mean?
keep in mind this book is absolutely terrible

4. Originally Posted by Dubulus
a. thats what my book says, but somehow i remember a way of figuring this out without doing an integral...
b. thats exactly what i thought, unfortunately it says nothing further than that. any ideas what it could possibly mean?
keep in mind this book is absolutely terrible
a. Unless you have memorised that $\Pr(X > \mu) = e^{-1}$ for an exponential distribution, you have to integrate.

b. Obviously the given event could be anything. The question is incomplete and as such is impossible to answer.