For each of the following cdfs F(x), find the pdf f(x) [pmf in part (d)], the 25th percentile, and the 60th percentile. Also, sketch the graphs of f(x) and F(x).
(a) F(x) = (1+e^−x)⁻¹ ,−∞ < x < ∞.
(b) F(x) = exp{−e^−x} ,−∞ < x < ∞.
(c) F(x) = 1/2 + 1/π tan⁻¹(x) ,−∞ < x < ∞.
(d) F(x) = Σ^x_j=1 (1/2)^j.