My Math Forum Probability

 November 17th, 2017, 01:30 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, 09:44 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,121 Thanks: 1101 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. $P[Y_m \text{ is max of }n] = \dfrac{(n-1)!}{n!} = \dfrac 1 n$

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