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Density Function and E(x)

  1. Nov 1, 2009 #1
    Density Function and E(x)[solved]

    The density function of X is given by

    https://webwork.math.lsu.edu/webwork2_files/tmp/equations/48/83b2bf602cc895a007a673a9a23c3c1.png

    If the expectation of X is E(X)=-1, find a and b.



    3. The attempt at a solution

    I'm actually working ahead of the class with this problem, so the material hasn't been covered, but I would like to figure it out. I know the equation for E(X), but don't know how to relate it to this problem. Please help.

    E(X)=∫xf(x)dx
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Nov 1, 2009 #2

    LCKurtz

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    You have two unknowns a and b, and you are given two conditions. f(x) is a density so what does that tell you? And you know E(x) value. Write down those two equations and solve for the unknowns a and b.
     
  4. Nov 1, 2009 #3
    - I haven't been able to figure it out with what you said. I know that the probability density function equation is the integral from a to b of f(x)dx, but I'm not sure how to relate that to the E(X) formula.
     
  5. Nov 1, 2009 #4

    LCKurtz

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    No. The probability density function is not "the integral from a to b of f(x)dx". The probability density function is f(x). But what do you know about probability density functions and their integrals? That will give you one equation in a and b. And the integral for E(x) = -1 will give you another.
     
  6. Nov 2, 2009 #5

    HallsofIvy

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    You must have
    [tex]\int_0^1 xf(x)dx= E(x)[/tex]
    and
    [tex]\int_0^1 f(x) dx= 1[/tex]

    Actually do those integrals with f(x)= a+ bx and solve the two equations for a and b.
     
  7. Nov 2, 2009 #6
    - Thanks. I wasn't quite grasping what i was being told at first, but as soon as you put both equations up, I knew what to do.
     
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