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Combination of Probability Density Functions

  1. Dec 13, 2012 #1
    Hi all,

    I need to calculate the probability density function [itex]f\left( Y \right)[/itex] of a function [itex]Y[/itex] of two variables [itex]A[/itex] and [itex]B[/itex] with known individual probability density functions [itex]f\left( A \right)[/itex] and [itex]f\left( B \right)[/itex]. What is the correct way to combine the PDF's?

    Specifically, I have a variable Y dependent on A and B by:

    [itex]Y = A + 2B[/itex]

    I know [itex]f\left( A \right)[/itex] and [itex]f\left( B \right)[/itex], how do I write [itex]f\left( Y \right)[/itex] in terms of [itex]f\left( A \right)[/itex] and [itex]f\left( B \right)[/itex]?

    Stats isn't my strong point so apologies if this is trivial!

  2. jcsd
  3. Dec 13, 2012 #2


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    Science Advisor

    The most direct way is to do it in two steps.
    Step 1: C = 2B (scale density function).
    Step 2: Y = A + C (convolution of density functions of A and C results in density function for Y).
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