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 Advanced Statistics Advanced Probability and Statistics Math Forum

 October 26th, 2013, 03:30 PM #1 Newbie   Joined: Oct 2013 Posts: 13 Thanks: 0 Exponential Random Variable Hi, I have a quick question. Let R and S be two independent exponentially distributed random variables with rates ? and ?. How would I compute P{S < t < S + R}? I am a little bit confused because of the variables on either side of the inequalities. I have tried conditioning on both S and R but I am not sure if I'm doing it right here. I can compute something like P{S < R} but the t is throwing me off! Any help is appreciated! October 26th, 2013, 06:28 PM #2 Senior Member   Joined: Feb 2013 Posts: 281 Thanks: 0 Re: Exponential Random Variable October 27th, 2013, 10:53 AM #3 Newbie   Joined: Oct 2013 Posts: 13 Thanks: 0 Re: Exponential Random Variable Thank you, I think I understand where that came from. What exactly are the function? Is it as simple as f(R) = L*exp(-LR) (L=lambda) and f(S)* = M*exp(-MS) (M=mu)? With the outer integral, should it be from 0 to infinity? As the exponential random variable isn't defined for below zero. Because doing this gives me M/(L-M)[exp(-Mt)-exp(-Lt)] which I'm not sure is correct because I want to show that M*P{S < t < S + R} = L*P{R < t < R + S}. October 28th, 2013, 02:47 PM #4 Newbie   Joined: Oct 2013 Posts: 13 Thanks: 0 Re: Exponential Random Variable Bump, I still can't progress. October 28th, 2013, 05:29 PM #5 Senior Member   Joined: Feb 2013 Posts: 281 Thanks: 0 Re: Exponential Random Variable I edited my post a bit. f(S) was not correct, it should be f(S,M). I think your result is okey. You can show this: L*P{S < t < S + R} = M*P{R < t < R + S}. (compare it with yours) October 28th, 2013, 07:04 PM #6 Newbie   Joined: Oct 2013 Posts: 13 Thanks: 0 Re: Exponential Random Variable Okay, I guess it could be a typo in the question. Should I get P{S < t < S + R} = M/(L-M)(exp(-Mt)-exp(-Lt))? October 29th, 2013, 03:23 AM #7 Senior Member   Joined: Feb 2013 Posts: 281 Thanks: 0 Re: Exponential Random Variable yes October 30th, 2013, 11:26 AM #8 Newbie   Joined: Oct 2013 Posts: 13 Thanks: 0 Re: Exponential Random Variable Thank you so much! Tags exponential, random, variable Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post MarcoEcon Algebra 3 November 19th, 2012 04:53 AM lawochekel Algebra 1 April 19th, 2012 12:39 PM eulerrules1 Advanced Statistics 0 December 13th, 2011 08:12 PM hoyy1kolko Algebra 1 November 5th, 2011 04:26 AM lordj0hn Advanced Statistics 3 July 11th, 2010 07:50 PM

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