Finding the first quartile of an exponential distribution.

**Evan.Kimia** · March 26th 2011, 11:30 AM

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!

**harish21** · March 26th 2011, 11:52 AM

Your cdf is WRONG.

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

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

then proceed towards your quartile

**Evan.Kimia** · March 26th 2011, 12:13 PM

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

**harish21** · March 26th 2011, 12:37 PM

$\beta - Q_1$

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

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