# Thread: Finding the first quartile of an exponential distribution.

1. ## Finding the first quartile of an exponential distribution.

I have a question asking to a.) find the first quartile of an exponential distribution and b.) seeing how far it is below the mean.

I get the integral of my distribution $\frac{1}{\theta }e\left( -\frac{x}{\theta } \right)$
and get

$-e\left( -\frac{x}{\theta } \right)$

from a previous section i see that to find the first quartile, you solve F(x)=.25
(in my book they use the notation F(pi sub .25)=.25

To solve i try to ln both sides which doesnt work since i have a negative number, so im doing something wrong. Anyone know howe i strayed? Thanks!

$F_X(x)$ is your cumulative distribution function(cdf).

And cdf = $\displaystyle F_{X}(x) = P(X \leq x) = \int_0^x f_X(x)\;dx$

3. Thanks! I figured it out. How could I tell how far away the first quartile would be from the mean given my answer?

4. $\beta - Q_1$

;where $\beta$ is the mean and $Q_1$ the first quartile.