1. Devise an algorithm to generate uniformly distributed points on the surface of a sphere (i.e., so that no area has a higher expected concentration than any other of the same size). Positions can be referenced by latitude and longitude.
2. Say an event happens at 60 times per hour in a Poisson distribution (say customer arrivals in a store), so averaging also once per minute. Devise an algorithm to generate realistic arrival times for a one-hour period.
Note: Assume what's available is a uniformly distributed random real number generator on the interval (0,1).