Consider a random interest rate R; paid in year i and another random interest rate R; paid in year j, with i j. Which of the following statements are correct? Tick all those that are correct but do not tick those that are incorrect. a. If R, and R; are uncorrelated then they are also statistically independent. b. Random interest rates R; are always lognormally distributed. C. In real markets, the assumption of statistically independent interest rates R; and R; is unrealistic. d. If R, and R, are statistically independent then they are also uncorrelated. e. The equation E(R₁ + R;) = E(R) + E(R;) holds only if R; and R; are statistically independent. f. The variance satisfies Var(a R;) = a² Var(R;) for any positive constant a.

Urban Travel Times Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, sent by residents driving to work. City Population N Driving time T Los Angeles 6489 16.8 Pittsburgh 1804 12.6 Washington 1808 14.3 Hutchinson 38 6.1 Nashville 347 10.8 Tallahassee 48 7.3 An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. a Construct a power model of driving time in minutes as a function of population measured in thousands b Is average driving time in Pittsburgh more or less than would be expected from its population? c If you wish to move to a smaller city to reduce your average driving time to work by 25, how much smaller should the city be?

is the following correct?

The table to the right classifies a stock's price change as up, down, or no change for both today's and yesterday's prices Price changes were examined for 104 days. A financial theory states that the price change of today for a stock must be independent of yesterday's price change. Test the hypothesis that daily stock price changes for this stock are independent. Let a=0.10. Price Change Previous Day Up No Change Down 16 Price Change Today 13 Up No Change 7 Down 14 16 10 13 Determine the null and alternative hypotheses for the test. Choose the correct answer below. O A. Ho: Today's price change and yesterday's price change are not independent. HA: Today's price change and yesterday's price change are independent. O B. Ho: Today's price change and yesterday's price change are independent. HA: Today's price change and yesterday's price change are not independent. OC. Ho: Today's price change and yesterday's price change have non-equal proportions. HA: Today's price change and yesterday's…