Proving the memoryless property of the exponential distribution


by DanielJackins
Tags: distribution, exponential, memoryless, property, proving
DanielJackins
DanielJackins is offline
#1
Nov19-12, 08:46 PM
P: 40
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?
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
haruspex
haruspex is offline
#2
Nov19-12, 11:40 PM
Homework
Sci Advisor
HW Helper
Thanks ∞
P: 9,215
P[(X ≤ a + b) ^ (X > a)] = P[X ≤ a + b] - P[X ≤ a] , right?
DanielJackins
DanielJackins is offline
#3
Nov20-12, 01:01 AM
P: 40
Thanks. Using that I was able to prove it. But why is what you said true?

haruspex
haruspex is offline
#4
Nov20-12, 02:25 AM
Homework
Sci Advisor
HW Helper
Thanks ∞
P: 9,215

Proving the memoryless property of the exponential distribution


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.


Register to reply

Related Discussions
Proving a matrix exponential determinant is a exponential trace Calculus & Beyond Homework 13
Proving a distribution is a member of generalised exponential family Set Theory, Logic, Probability, Statistics 6
Property of exponential functions Precalculus Mathematics Homework 4
Proving memoryless property. Calculus & Beyond Homework 1
Exponential growth and exponential distribution Set Theory, Logic, Probability, Statistics 3