3) To estimate the quality and price of bars in the D.C. area, 1,500 bars are randomly selected and rated on a scale of 1 to 3 for quality (1 being low quality and 3 being high quality) and a scale of 1 to 5 for price (1 being cheap and 5 being expensive). The results were as follows: Price 1 2 3 4 5 76 99 104 69 70 Quality 122 131 111 155 56 117 70 220 56 44 a) Build a joint probability table based on this data set. b) What is the probability that a bar selected at random will have a price of greater than or equal to 2 and a quality of 2? c) What is the expected quality of a randomly selected bar in D.C.? d) What is the expected price of a randomly selected bar in D.C.? e) What is the covariance of quality and price for bars in D.C.? f) What is the correlation between quality and price for bars in D.C.? g) Does the correlation make sense to you? That is, would you expect the price and quality of bars in DC to have a positive, negligible, or negative relationship? Consider drawing on your own experience (Don't overthink your answer, there is not correct answer)