1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    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).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Combination of Probability Density Functions