My Math Forum Probability
 User Name Remember Me? Password

 Advanced Statistics Advanced Probability and Statistics Math Forum

 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: 2,266 Thanks: 1198 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. $P[Y_m \text{ is max of }n] = \dfrac{(n-1)!}{n!} = \dfrac 1 n$

 Thread Tools Display Modes Linear 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

 Contact - Home - Forums - Cryptocurrency Forum - Top