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!

Area under the curve - probability

  1. Jun 26, 2010 #1
    It's something that I know but I've never been able to figure out 'why?' Why is does the area underneath the normal distribution (or any distribution) represent probability?

    Thank you.

    M
     
  2. jcsd
  3. Jun 26, 2010 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The short answer to your question is the definition:

    A nonnegative function f(x) is said to be the density function for the continuous random variable X if for all real numbers a < b:

    [tex]P(a\le X \le b) = \int_a^b f(x)\, dx[/tex]

    From calculus we know the integral on the right represents the area under f(x) between a and b. Since the cumulative distribution function is given by

    [tex]P(X \le x) =\int_{-\infty}^{x} f(t)\, dt[/tex]

    it follows that

    [tex]\int_{-\infty}^{\infty} f(x)\, dx = 1[/tex]

    Putting these together shows why the area under the curve represents probability. Does that explanation help or did you already know that?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Area under the curve - probability
Loading...