Question: Suppose stop lights at an intersection alternately show green for one minute, red for one minute (ignore amber). Suppose a car arrives at the lights at time distributed uniformly at random relative to this cycle. Let X be the delay of the car at the lights, neglecting any delay due to traffic congestion.
a) Find a formula for the c.d.f. of x, and sketch its graph.
b) Is X discrete, discrete, continuous, or neither? C) Find E(X) and Vαr(X).
c) Suppose that the car encounters a succession of ten such stop lights. Make an independence assumption and use the normal approximation to estimate the probability that the care will be delayed more than four minutes by the lights.