November 17th, 2017, 02:30 PM #1 Member   Joined: Nov 2016 From: Kansas Posts: 73 Thanks: 1 Probability Suppose A$_1$,A$_2$,... are independent random variables with the uniform distribution in [0,1]. We say that n is a record if: A$_n$ $\geq$ A$_m$ for all 1 $\leq m \leq$ n 1.Show that the probability of the event Y$_n$ that n is a record is P[Y$_n$]= 1/n 2.Let Z denote the event that there are infinitely many records. Show that P [Z] is zero or one. November 17th, 2017, 10:44 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,649 Thanks: 1476 for (1) As all the $Y_k$'s are identical all the possible orderings of them are equiprobable. For a given $Y_m$ there are $(n-1)!$ orderings where $Y_m$ is the max. There are a total of $n!$ orderings. $P[Y_m \text{ is max of }n] = \dfrac{(n-1)!}{n!} = \dfrac 1 n$ Tags probability, random variable, record 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 rivaaa Advanced Statistics 5 November 5th, 2015 02:51 PM hbonstrom Applied Math 0 November 17th, 2012 08:11 PM token22 Advanced Statistics 2 April 26th, 2012 04:28 PM naspek Calculus 1 December 15th, 2009 02:18 PM

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