Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Confusion over using integration to find probability

  1. Jun 27, 2017 #1
    Hey everyone, first, let me say I understand the complement rule. Where I am confused is over the integration. My professor said that suppose you have a continuous cumulative distribution function F(x) = 1-e-x/10, if x > 0 (0, otherwise). And suppose you want to find P(X>12) you can use the complement rule 1-P(X<=12). Which is equivalent to 1-F(12) [note he said this works for all cases, not just this example].

    My question is why isn't it 1-[F(12) - F(0)]?

    This is really tripping me up. If your x can take all probabilities from 0 to 12, don't you want to find the area from 0 to 12 and not just F(12)?

    I know this is a method of simplifying the integral since you have an improper integral and have to evaluate a limit (supposing you don't use the compliment rule). But why does this work for all cases?
     
    Last edited: Jun 27, 2017
  2. jcsd
  3. Jun 27, 2017 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    What value does F(0) take?

    Edit: Also, the cdf F(x) is the probability of taking any value less than or equal to x. By definition, you therefore have P(X ≤ 12) = F(12).
     
  4. Jun 27, 2017 #3
    In this case 1 - 1 = 0. Meaning that you have 1 - [F(12) - 0], in this case. But he said it is true for all cases...
     
  5. Jun 27, 2017 #4

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Read my edit above.
     
  6. Jun 27, 2017 #5
    I guess, why is this the definition? Perhaps this is more calculus related and I'm not remembering. It seems vaguely familiar. I guess it relatively makes sense since F(A) - F(B) would be the area between the two points. Then F(A) would be the entire area up until A since you'd have no lower bound.
     
  7. Jun 27, 2017 #6

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Like most defined things, it is defined because it is useful.

    Indeed, F(B)-F(A) would be equal to P(A<X≤B).
     
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: Confusion over using integration to find probability
  1. Probability confusion (Replies: 2)

Loading...