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 July 7th, 2019, 08:45 AM #1 Newbie   Joined: Jul 2019 From: kazahstan Posts: 2 Thanks: 0 Number of trials until success for successful participants Hello, I have the following problem: Given a Bernoulli trial with probability of success p and a number of trials x, what is the expected number of trials until success among those that succeed in x trials? e.g. if p = 0.02 and x = 60, (1-0.02)^50 = 0.36 attempts fail all 60 trials, and I would like to find the expected number of trials the successful ones take until success. I understand it is lower than 1/0.02 and will decrease with x but don't know how to proceed. I think it's simple and I'm missing something basic, anyway thanks ahead ! Last edited by mikimiki1; July 7th, 2019 at 08:51 AM. July 7th, 2019, 09:52 AM #2 Newbie   Joined: Jul 2019 From: kazahstan Posts: 2 Thanks: 0 Better phrased: I have the following problem: Given a Bernoulli trial with probability of success p and a number of trials x, what is the expected number of trials until success in a case success was achieved in x trials? e.g. if p = 0.02 and x = 60, I would like to find the expected number of trials taken in case of succes within 60 trials. I understand it is lower than 1/0.02 and will decrease with x but don't know how to proceed. I think it's simple and I'm missing something basic, anyway thanks ahead ! July 7th, 2019, 11:11 AM #3 Senior Member   Joined: Sep 2015 From: USA Posts: 2,553 Thanks: 1403 Assuming we stop after success, and that we know success occurred within $n$ trials we have $P[k] = \dfrac{p(1-p)^{k-1}}{1-(1-p)^n}, ~1 \leq k \leq n$ $E[K]=\sum \limits_{k=1}^n k P[k] = \Large \frac{n p (1-p)^n+(1-p)^n-1}{p \left((1-p)^n-1\right)}$ Tags number, participants, success, successful, trials 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 Zeus579 Probability and Statistics 2 March 2nd, 2016 05:10 AM butabi Advanced Statistics 0 April 14th, 2012 07:56 AM realfunboy Advanced Statistics 3 October 31st, 2009 12:00 PM Cat Math Events 8 July 13th, 2009 05:34 AM hales Algebra 2 September 20th, 2007 08:16 AM

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