Theorem: If X is a continuous random variable and g is a function, then
Example. You throw a dart at a circular board of radius 1 ft. It hits a point on the board uniformly at random, and you win \frac{1}{r}r$ ft from the center. What are your expected winnings?
where X = distance of point to center, 2}$
Example. Suppose is a r.v. w/ cdf . Is discrete or continuous? If so, calculate (i) the mean of , (ii) , and (iii) .
continuous and piecewise continuously differentiable is a continuous r.v.
(i)
(ii)
(iii)