1. A traffic engineer is investigating a new transit system for Illinois. Define the following random variables for the propsed system: X = number of lanes reserved for automobile traffic on a random transit way. . Y = number of lanes reserved for bicycle traffic on a random transit way. The joint probability distribution is given as: f(x, y) * =0 x = 2 X =4 y= 0 0.05 0.1 0.1 0.1 0.2 0.2 0.05 0.1 0.1 a) Determine the probability that a random transit way has 2 lanes for automobiles and 1 lane for bicycles. b) Determine the probability that a random transit way has 2 lanes for automobiles. c) Determine the probability that a random transit way has 2 lanes for bicycles. d) A randomly selected road has no bicycle lanes. Determine the probability that this road has 2 lanes for automobiles. e) Determine the probability that a random transit way has more than 2 lanes of any type (i.e. for bicycles OR automobiles). 2. The joint probability density function (p.d.f.) for continuous random variables X and Y is: f (x, y) = 10, OSx1,0 sys2 elsewhere a) Determine P(Y 0.5). b) Determine P(Y