Consider the triangle with vertices (0; 0), (1; 0) and (0; 1). Let Z be a uniform
random variable in the interval [0; 1]. Draw a vertical line that intersects the x axis at Z. This
line divides the triangle in two pieces. Select a point (X; Y ) uniformly at random from the right
piece. Find the expectation E[X] of the x coordinate of the selected point.
Hint: You might have to integrate an ugly looking function. Factor the numerator, cancel
stu� and simplify the function.