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

Proving the memoryless property of the exponential distribution

  1. Nov 19, 2012 #1
    Given that a random variable X follows an Exponential Distribution with paramater β, how would you prove the memoryless property?

    That is, that P(X ≤ a + b|X > a) = P(X ≤ b)

    The only step I can really think of doing is rewriting the left side as [P((X ≤ a + b) ^ (X > a))]/P(X > a). Where can I go from there?
     
  2. jcsd
  3. Nov 19, 2012 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    P[(X ≤ a + b) ^ (X > a)] = P[X ≤ a + b] - P[X ≤ a] , right?
     
  4. Nov 20, 2012 #3
    Thanks. Using that I was able to prove it. But why is what you said true?
     
  5. Nov 20, 2012 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    X has three disjoint ranges, <a, (a,a+b), >a+b.
    P[(X ≤ a + b) ^ (X > a)] is the probability X is in the middle range.
    P[(X ≤ a + b)] is the probability X is in the first or middle range.
    P[X ≤ a] is the probability X is in the first range.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook