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## Homework Statement

IF X has an exponential distribution with parameter [itex]\lambda[/itex], derive a general expression for the (100p)th percentile of the distribution. Then specialize to obtain the median.

## Homework Equations

[tex]X.exp(\lambda)=\lambda e^{-\lambda x} for x>0[/tex]

[tex]p=F(\eta (p)) = \int_{-\infty}^{\eta (p)} f(y)dy[/tex]

## The Attempt at a Solution

First, can I verify that this antiderivative is correct?

Since F'(X) = f(X) [tex]F(X)=-e^{-\lambda x}[/tex]

Finding the 100pth percentile is equivalent to finding the cumulative density function (the antiderivative) from 0-->p correct?

And F(.5) = [itex]\eta[/itex] for the mean...

I'm really confused on how to set this up and what i'm looking for. Any help would be great.