1. Not finding help here? Sign up for a free 30min 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!

'Triangular Distributions' Probability Density Function

  1. Oct 9, 2008 #1
    (\Triangular" distributions.) Let X be a continuous random variable with prob-
    ability density function f(x). Suppose that all we know about f is that a </= X </= b,
    f(a) = f(b) = 0, and that there exists a value c between a and b where f is at a maxi-
    mum. A natural density function to consider in this case is a piece-wise linear function,
    corresponding to lines connecting (a; 0) with (c; f(c)), and (c; f(c)) with (b; 0).
    a) What is the value of f(c)?
    b) Sketch a graph of f(x).
    c) Compute the expected value E(X) and the variance Var(X).

    I have not been given any numbers and am very confused as to how there could be a numerical answer to this question. I know the probability density function looks like a triangle, with f(a) and f(b) on the x-axis, but am not sure where to go with this. Anyone have a suggestion?
     
  2. jcsd
  3. Oct 9, 2008 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    The density function will look like:

    f(x)=K(x-a) a<x<c
    f(x)=L(b-x) c<x<b

    where L and K are determined by:
    L(b-c)=K(c-a)
    integral from a to b of f(x)=1.

    Your results will be functions of a, b and c, so don't expect to get numbers unless a, b, and c are specified.
     
    Last edited: Oct 10, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?