3.3 Functions ofrandom variables. Two emergency response units patrol uniformly and independently a 10-mile stretch of road. An emergency incident occurs on the roadway and its position is uniformly distributed, independent of the positions of the response units. The incident requires both response units to be dispatched to the scene. Call the two units unit a and unit b. Assume that response speed is fixed at 10 mph and that U-turns are permitted.

a. Determine the mean travel time for unit a to reach the scene.

b. Determine the mean time until the first unit (either a or b) reaches the scene.

c. Determine the probability density function for the time until the second unit reaches the scene.