Question

Consider the following data on automobile trips in the area of Washington, D.C., for 1970. The measurements are in hundreds of trips per day, 1 Destination A.C. F.С. P.W.C. Other Total Origin (1) Arlington Co. (2) Fairfax Co (3) Prince William Co. 34.6 29.0 3.1 5.4 62.8 0.2 1.1 18.2 45.9 10.0 121.1 86.1 65.2158.1 38.2 282.4 Total 66.7 75.1 19.5 Let [X= i] be the event “ the trip origin is area i," i-1, 2, 3, and let [Y=] be the event "the trip destination is area j," j= 1,2,3,4. Assume that one can assign probabilities to the events using a relative frequency definitiorn based on the numbers in the above table. Thein (a) Test if X and Y are independent. (b) Compute Pr[X- i] for i-1,2,3. (c) Compute Pr[Y-j] for j 1, 2, 3, 4. (d) Compute PHY-IX-i] for i -1, 2, 3 and j 1, 2, 3, 4. (e) Compute PriX-Y- for1,2,3 and j-1,2,3,4 using Bayes' theorem (f) Using the context of this example explain the difference between

Answer 1