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Math Help - Percentiles in a Continous Random Variable distribution

  1. #1
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    Percentiles in a Continous Random Variable distribution

    The probability density function of x is:
    f(x) = 4x(1-x^2) when x is a value between 0 and 1. (0 and 1 are included)
    = 0 otherwise
    What is the 75th percentile of this distribution?
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    the 75th percentile is the the x that gives the answer f=0.75 I believe
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  3. #3
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    Quote Originally Posted by Pink Lady View Post
    The probability density function of x is:
    f(x) = 4x(1-x^2) when x is a value between 0 and 1. (0 and 1 are included)
    = 0 otherwise
    What is the 75th percentile of this distribution?
    By definition:

    Find the value of a such that \int_0^a 4x (1 - x^2) \, dx = 0.75.

    Quote Originally Posted by Flyingdutchman View Post
    the 75th percentile is the the x that gives the answer f=0.75 I believe
    Sorry but that's not correct.
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  4. #4
    MHF Contributor matheagle's Avatar
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    It's F(a)=.75, not f(a)=.75.
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    P(X \leqslant a) = \left\{ {\begin{array}{*{20}c}<br />
   {0,} & {a \leqslant 0}  \\<br />
   {\int_0^a {4x(1 - x^2 )dx,} } & {0 < a \leqslant 1}  \\<br />
   {1,} & {1 < a}  \\ \end{array} } \right.
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  6. #6
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    yeah sorry about that, F, F, F, F!!! Bad dutchman!
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  7. #7
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Flyingdutchman View Post
    yeah sorry about that, F, F, F, F!!! Bad dutchman!
    don't F me
    sry another bad pun
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