My Math Forum Drawing balls with repetition

 November 25th, 2011, 01:21 PM #1 Member   Joined: Sep 2010 Posts: 60 Thanks: 0 Drawing balls with repetition There are n balls in an urn. We draw $a_n$ balls from the urn with repetition. (i) What is the probability of drawing the ith ball at least twice? (ii) For which value of $a_n$ will the order of magnitude of the expected number of the at least twice drawn balls be $Cn^{\alpha}, \; \alpha \in \mathbb{R}$? Specially, for $\alpha=0$ what is $a_n$? (iii) What are the potetnial (possible) $\alpha$ exponents? Any help would be appreciated! Thank you very much!
 November 27th, 2011, 08:19 AM #2 Member   Joined: Sep 2010 Posts: 60 Thanks: 0 Re: Drawing balls with repetition For (i) is the answer: $1-\left(\frac{n-1}{n}\right)^{a_n} - n \left(\frac{n-1}{n}\right)^{a_n-1} \frac{1}{n}$? And what is the answer for (ii) and (iii)? I would be grateful for any help!

 Tags balls, drawing, repetition

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Skyer Algebra 3 January 6th, 2014 11:26 AM daigo Algebra 2 July 8th, 2012 09:47 AM SabinManiac Advanced Statistics 0 February 1st, 2012 07:08 AM divide Real Analysis 0 October 11th, 2010 12:55 PM byron123 Advanced Statistics 2 September 10th, 2008 09:39 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top