My Math Forum Uniform Joint Distribution

 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 $\displaystyle E(X|y)=\frac{1}{y}\int_0^y xdx=\frac{y}{2}$ $\displaystyle E(X)=\int_0^1 E(X|y)dy=\frac{1}{4}$

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