For which values of a does $\int_0^\infty e^{ax} dx$ converge?
Find a constant C such that p is a probability density function on the given interval, and compute the probability indicated.
(a) p(x) = Cx(8 - x) on [0, 8]; P(3 ? X ? 4)
(b) p(x) = \frac{C}{\sqrt{1 - x^2}} on [-1, 1]; P(-\frac{1}{2} ? X ? \frac{1}{2})
(c) p(x) = Ce^{-e^{-x}}e^{-e^x} on (-?, ?); P(-4 ? X ? 4)