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!

Cumulative distribution and density functions

  1. May 1, 2013 #1
    1. The problem statement, all variables and given/known data

    Let X be a random variable with probability density function:

    0.048(5x-x2) IF 0 < x < 5

    0 otherwise

    Find the cumulative distribution function of X

    a) If x ≤ 0, then F(x) =

    b) If 0 < x < 5, then F(x) =

    c) If x ≥ 5, then F(x) =

    2. Relevant equations

    Not quite sure

    3. The attempt at a solution

    The answer to a) is 0. The answer to c) is 1.

    I am making the reasonable assumption that a) is 0 because there is no probability at that point, and that c) is 1 because after that, all probability has been "used" so to speak. However, integrating the function between 0 and 5 does not work. It seems as if my professor totally skipped over teaching us this particular type of problem. Statistics usually makes a good deal of sense to me, but this is pretty foreign.
     
  2. jcsd
  3. May 1, 2013 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You say "integrating the function between 0 and 5 does not work". What about it does not work?

    In fact, if we define f(x) = 0 for x < 0 and for x > 5, then the cumulative distribution F(z) is
    [tex] F(z) = \int_{-\infty}^z f(x) \, dx \\
    = 0 \; \text{ if } z < 0,\\
    = \int_0^z (48/1000)(5x - x^2) \, dx \; \text{ if } 0 \leq z \leq 5,\\
    = 1 \; \text{ if } z > 5.[/tex]
    Do the integration to see what you get.

    Are you sure your course notes or textbook do not have any similar examples?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Cumulative distribution and density functions
Loading...