Let p=E(X), o=stanard deviation of X. Find the probability P(p-o SX s p+o) if X has... a. ... a Binomial distribution with n=11 and p=2/7. b. ... a Geometric distribution with p = 0.41. C. ... a Poisson distribution with A = 8. Let f: R R be a differentiable function whose graph z = f(x,y) intersects every vertical plane y = \x in a straight line. (a) Show that f is a linear function f(x, y) = ax + by + c. (b) Can the differentiability hypothesis be weakened (for example, to continuity)?