Question

John walks at a speed (miles/hr) that is uniformly distributed on the interval [A,B], where A is uniformly distributed on the interval [0,2] and B is uniformly distributed on the interval [1,3]. The distance between John's apartment and school is 1.5 miles. What is the expected time that John will spend on the road on his way back to his apartment?

Answer 1

Expected value of A = (0+2)/2 = 1

Expected value of B = (1+3)/2 = 2

So expected interval [A,B] = [ 1,2]

Expected value of speed = (1+2)/2 = 1.5 miles /hr

Expected time = distance / expected speed = 1.5/1.5 = 1 hr