1. Consider two farmers, one who owns land and the other who rents it from someone else. In good times (which happen with probability 0.3), the owner-farmer earns an income of 125. In bad times (which happen with probability 0.7), he earns an income of 75. The tenant works on a farm that is twice as large and earns an income of 250 in good times (prob=0.3) and 150 in bad times (prob=0.7).

   1. However, he must pay a rent of 100. Calculate the expected net income of both farmers.

   2. Assume that their utility function takes the following form: ? = ?1/2, where ?stands for the farmer’s net income. Calculate the expected utility of both.

   3. Compare this result to the calculation on expected income. What do you conclude in terms of the different risks that both farmers face?

The accompanying table provides data for​ tar, nicotine, and carbon monoxide​ (CO) contents in a certain brand of cigarette. Find the best regression equation for predicting the amount of nicotine in a cigarette. Why is it​ best? Is the best regression equation a good regression equation for predicting the nicotine​ content? Why or why​ not?

1. Find the best regression equation for predicting the amount of nicotine in a cigarette. Use predictor variables of tar​ and/or carbon monoxide​ (CO). Select the correct choice and fill in the answer boxes to complete your choice. ​(Round to three decimal places as​ needed.)

A. Nicotine = ____ + (____) CO

B. Nicotine = ____ + (____) Tar

C. Nicotine = ____ + (____) Tar + (____) CO

2. Why is this equation best?

A. It is the best equation of the three because it has the lowest adjusted R2​, the highest​ P-value, and only a single predictor variable.

B. It is the best equation of the three because it has the highest adjusted R2 the lowest​ P-value, and only a single predictor variable.

C. It is the best equation of the three because it has the lowest adjusted R2​, the highest​ P-value, and removing either predictor noticeably decreases the quality of the model.

D. It is the best equation of the three because it has the highest adjusted R2​, the lowest​ P-value, and removing either predictor noticeably decreases the quality of the model.

3. Is the best regression equation a good regression equation for predicting the nicotine​ content? Why or why​ not?

A. ​No, the large​ P-value indicates that the model is not a good fitting model and predictions using the regression equation are unlikely to be accurate.

B. Yes, the small​ P-value indicates that the model is a good fitting model and predictions using the regression equation are likely to be accurate.

C. No, the small​ P-value indicates that the model is not a good fitting model and predictions using the regression equation are unlikely to be accurate.

D. ​Yes, the large​ P-value indicates that the model is a good fitting model and predictions using the regression equation are likely to be accurate.

1. Suppose a car driven under specific conditions gets a mean gas mileage of 40 miles per gallon with a standard deviation of 3 miles per gallon. On about what percentage of the trips will your gas mileage be above 43 miles per gallon?

A.About 68%, because 43 miles per gallon is 2 std. deviations above the mean. By the 68-95-99.7 rule, about 68% of the distribution lies within 2 std. deviations of the mean.

B.About 68%, because 43 miles per gallon is 1 std. deviation above the mean. By the 68-95-99.7 rule, about 68% of the distribution lies within 1 std. deviation of the mean.

C.About 16%, because 43 miles per gallon is 1 std. deviation above the mean. By the 68-95-99.7 rule, about 16% of the distribution lies within 1 std. deviation of the mean.

D.About 2.5%, because 43 miles per gallon is 2 std. deviations above the mean. By the 68-95-99.7 rule, about 2.5% of the distribution lies within 2 std. deviations of the mean.

E.About 16%, because 43 miles per gallon is 1 std. deviation above the mean. By the 68-95-99.7 rule, about 68% of the distribution lies within 1 std. deviation of the mean. So 32% lies outside of this range, 16% in each tail.

F.About 2.5%, because 43 miles per gallon is 2 std. deviations above the mean. By the 68-95-99.7 rule, about 95% of the distribution lies within 2 std. deviations of the mean. So 5% lies outside of this range, 2.5% in each tail.

2.Assume that a set of test scores is normally distributed with a mean of 80 and a standard deviation of 25. Use the 68-95-99.7 rule to find the following quantities.

a. The percentage of scores less than 80 is ___________%. (Round to one decimal place as needed.)

b. The percentage of scores greater than 105 is _____________%. (Round to one decimal place as needed.)

c. The percentage of scores between 30 and 105 is ___________%.(Round to one decimal place as needed.)

3.Working with equal sample sizes, researchers compared three new cold remedies to a placebo. Which remedy is most likely to be most effective? Explain.

A.The one that gave results statistically significant at the 0.01 level, because the remedy was successful in so many people that the chance of at least this much success would be greater than 0.01, if the remedy were no better than the placebo.

B.The one that gave results that were not statistically significant, because the other tests do not produce positive results.

C.The one that gave results that were not statistically significant, because statistically significant results would indicate that the test was not performed correctly.

D.The one that gave results statistically significant at the 0.05 level, because the remedy was successful in so many people that the chance of at least this much success would be greater than 0.05, if the remedy were no better than the placebo.

E.The one that gave results statistically significant at the 0.01 level, because the remedy was successful in so many people that the chance of at least this much success would be less than 0.01, if the remedy were no better than the placebo.

F.The one that gave results statistically significant at the 0.05 level, because the remedy was successful in so many people that the chance of at least this much success would be less than 0.05, if the remedy were no better than the placebo.

When coding in R Studio

install.packages("hflights")
library(hflights)

if filter for flights >= 3000 miles how many flights in new dataframe

1D Array Function

Write a function in MATLAB to convert miles to feet. This function should work for one number, or an array of numbers to be converted.

Develop and test a Python program that converts pounds to grams, inches to centimeters, and kilometers to miles. The program should allow conversions both ways.

In each of problems 1 through 4: (a) Find approximate values of the solution of the given initialvalue problem at t=0.1, 0.2, 0.3, and 0.4 using the Euler methodwith h=0.1 (b) Repeat part (a) with h=0.05. Compare the results with thosefound in (a) (c) Repeat part (a) with h=0.025. Compare the results with thosefound in (a) and (b). (d) Find the solution y=φ(t) of the given problem and evaluateφ(t) at t=0.1, 0.2, 0.3, and 0.4. Compare these values with the results of (a), (b), and (c). 3. dy/dt = 0.5 -t +2y, y(0) = 1 Please also provide solution using Matlab.

Amir Labib gets a reduced rate from his auto insurance company because he represents in his application that he commutes less than ten miles a day to work. Three years later, he and his wife buy a new residence, farther away from work, and he begins a fifteen-mile-a-day commute. The rate would be raised if he were to mention this to his insurance company. The insurance company sees that he has a different address, because they are mailing invoices to his new home. But the rate remains the same. Amir has a serious accident on a vacation to Yellowstone National Park, and his automobile is totaled. His insurance policy is a no-fault policy as it relates to coverage for vehicle damage. Is the insurance company within its rights to deny any payment on his claim? How so, or why not?

In 2009, Peter Calhoun gets a life insurance policy from Northwest Mutual Life Insurance Company, and the death benefit is listed as $250,000. The premiums are paid up when he dies in 2011 after a getaway car being chased by the police slams into his car at fifty miles per hour on a street in suburban Chicago. The life insurance company gets information that he smoked two packs of cigarettes a day, whereas in his application in 2009, he said he smoked only one pack a day. In fact, he had smoked about a pack and a half every day since 1992. Is the insurance company within its rights to deny any payment on his claim? How so, or why not?