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 Advanced Statistics Advanced Probability and Statistics Math Forum

 November 3rd, 2017, 02:46 PM #1 Senior Member   Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0 Distribution of Function of Random Vector N, K, and i are positive integers for the following: Let the random vector X be represented by , where X1, X2, ... XN are all random variables which follow a discrete uniform distribution with parameters 1 and K. Hence, P(Xi = xi) = 1/K on 1 <= xi <= K for 1 <= i <= N. Let the random variable Y = f(X vector) = the number of distinct entries in X vector. So, for example, if N = 3 and K = 9: f(<1, 1, 1>) = 1 f(<1, 2, 1>) = 2 f(<1, 2, 3>) = 3 f(<3, 1, 3>) = 2 f(<9, 9, 9>) = 1 f(<1, 8, 8>) = 2 etc. What is the distribution of Y? My attempt so far: I believe that X vector follows a Multinomial Distribution with parameters N and the correspondingly sized probability vector <1/K, ... , 1/K>. This may be helpful. I also think that the support of Y is the set of all integers between 1 and N (inclusive). But I get lost from this point; I'm still nowhere near finding the distribution of Y. Do you have any ideas? November 3rd, 2017, 10:36 PM #2 Senior Member   Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0 Figured it out after writing a bit of python code: http://prntscr.com/h61pen Crazy stuff. Tags distribution, function, random, vector 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 John Travolski Advanced Statistics 1 October 26th, 2017 08:42 PM frankpupu Advanced Statistics 2 March 1st, 2012 03:45 AM manixrock Algebra 2 April 11th, 2009 02:56 AM begyu85 Algebra 3 February 19th, 2008 01:34 PM JesusGumbau Algebra 9 December 21st, 2007 04:01 AM

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