Problem 6: Re-location Congratulations, you have finished your MBA and accepted a new job in your dream city, Wannahockaloogee. As part of your re-location, you are trying to decide on a new apart- ment. You've never lived in Wannahockaloogee before, so you aren't sure which amenities will be the most important to you once you have settled in. Based on your previous ex- perience, however, you have some sense of your preferences. Now that you understand the importance of uncertainty, you came up with the following table: Amenity Low =0 Medium = 1 High = 2 Low rent 0% 20% 80% Pool 50% 40% 10% Close to work 10% 20% 70% Food/entertainment nearby 50% 0% 50% This table reads as follows: The probability that once you settle in, price has high impor- tance is 80%, or P(Low rent = 2) = 0.8. (For example, maybe after you've settled in and gotten to know the city, you realize that paying more for rent just isn't worth it, and you just don't use the pool all that much. In this case, "low rent" would have high importance and "pool" would have low importance.) Based on your table: (a) Compute the expected value of each amenity. (b) Compute the variance of each amenity. (c) Besides price, which amenity should you place the highest weight on and why? (d) Besides price, which amenity should you place the lowest weight on and why?Problem 7: Normal probabilities X ~ N(-2,9) (Read X distributed Normal with mean -2 and variance 9) Compute: (i) P(X > -2) (ii) P(X > -2 + v9) (iii) P(X = 3) (iv) Express P(-8