Question: A random point x = ( x , Y ) ?is drawn uniformly from the triangle in the xy plane depicted below. ( a )

A random point x $= ($ x $,$ Y $)$ ?is drawn uniformly from the triangle in the xy plane depicted below.

$($ a $)$ ?Determine the values E $($ X $)$ ?and E $($ XY $) . ($ Lead: Show that the conditional expectation E $($ X $|$ Y $) = 0$ ?for all Y in $[0, 2] .)$

$($ b $)$ ?Determine the variance matrix K $=$ ?V $($ X $)$ ?of the vector X $= ($ X $,$ ?Y $)$

-1 2 Y (X,Y) 1 X

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