March 13th, 2016, 06:38 PM #1 Senior Member   Joined: Jan 2014 Posts: 196 Thanks: 3 Uniform Joint Distribution Suppose Y is uniformly distributed on (0, 1), and that the conditional distribution of X given that Y = y is uniform on (0, y). Find E[X] and Var(X). Not sure how to put this one together since it is a joint distribution. Here is my attempt so far. $\displaystyle f_Y(y)=1$ , for $\displaystyle 0 \leq y \leq 1$ for $\displaystyle X$ to be uniform on $\displaystyle (0,y)$ $\displaystyle f_{x|y}(x,y)=1/y$ , for $\displaystyle 0 \leq x \leq y$ so does $\displaystyle E[X] = \frac{y-0}{2} = \frac{y}{2}=\frac{1}{2}$ ?? Am I starting this off right? Thank you for any help! March 14th, 2016, 03:57 PM #2 Global Moderator   Joined: May 2007 Posts: 6,856 Thanks: 745 $\displaystyle E(X|y)=\frac{1}{y}\int_0^y xdx=\frac{y}{2}$ $\displaystyle E(X)=\int_0^1 E(X|y)dy=\frac{1}{4}$ Tags distribution, joint, uniform 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 loveinla Probability and Statistics 1 August 19th, 2015 01:59 PM huntersilias Probability and Statistics 1 November 17th, 2014 02:00 PM batman350z Advanced Statistics 3 April 23rd, 2012 03:50 PM 450081592 Advanced Statistics 0 January 24th, 2012 08:44 PM sletcher Calculus 18 December 15th, 2010 12:51 PM

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