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Median of a Density Function

  1. Nov 2, 2008 #1
    1. The problem statement, all variables and given/known data
    The probability density function is defined as

    f(x) = (4/81)x(9-x^2) for 0 <= x <= 3
    = 0 for every other value

    Find the median value of the density.

    2. Relevant equations
    The median of a function is

    integral from m to infinity of f(x)dx = 1/2


    3. The attempt at a solution

    I took the integral from m to 3 of (4/81)x(9-x^2).

    This turned out to be

    (18/81)x^2 -(1/81) x^4 = 1/2

    I then evaluated the left hand side from m to 3 and simplified so that only the variable m is left. The equation I got was

    (1/81)m^4 - (18/81)m^2 = -1/2

    I know that I am suppose to solve for m in order to get the median but I'm not sure how to do this, and I am also unsure whether my procedure is correct.

    Any help would be great thanks. Sorry bout the formatting I'm new to this.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 2, 2008 #2

    statdad

    User Avatar
    Homework Helper

    The integral looks okay. In the equation try setting

    [tex]
    u = m^2 \Rightarrow u^2 = m^4
    [/tex]

    Then solve the quadratic for [tex] u [/tex], and find [tex] m [/tex] from that. Remember that [tex] m [/tex] has to be between 0 and 3.
     
  4. Nov 2, 2008 #3
    Thanks a lot, I tried that out and it works
     
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