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Proving the memoryless property of the exponential distribution 
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#1
Nov1912, 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 + bX > 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
Nov1912, 11:40 PM

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P[(X ≤ a + b) ^ (X > a)] = P[X ≤ a + b]  P[X ≤ a] , right?



#3
Nov2012, 01:01 AM

P: 40

Thanks. Using that I was able to prove it. But why is what you said true?



#4
Nov2012, 02:25 AM

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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. 


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