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Math Help - Finding the first quartile of an exponential distribution.

  1. #1
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    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!
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  2. #2
    MHF Contributor harish21's Avatar
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    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
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  3. #3
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    Thanks! I figured it out. How could I tell how far away the first quartile would be from the mean given my answer?
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  4. #4
    MHF Contributor harish21's Avatar
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    \beta - Q_1

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