Suppose an analyst takes a random sample of 5 recent truck shipments made by a company and records the distance in miles and delivery time in days that the shipment was made available for pick-up.
The observations are as follows:
Distance (miles) 825 215 1070 550 340
Delivery time (days) 2 1 4 2 1
Determine the covariance between the two variables. Use the sample covariance formula:
One of the major risks in the economy is the oil price. Many financial assets are severely affected by the oil price. Consider a natural gas company and an automobile company. The natural gas company will be hit by a low oil price because the demand for natural gas will decrease as oil becomes cheaper. But the automobile company will benefit from a low oil price as more people can afford the cost of driving a car. The probability of the oil price next year is given by the following table:
Oil price Probability
does not change 40%
Contingent on the change in the oil price next year, the annual returns to the companies are expected as follows:
If oil price Natural gas Automobile
drops -8% 14%
does not change 7% 4%
arises 12% -6%
You are planning to invest 40% of your investment in the natural gas company and the remaining in the automobile company. What is the variance of your portfolio?
After analyzing several months of sales data, the owner of an appliance store produced the following probability distribution of the number of refrigerators and stoves sold daily.
Refrigerators Stoves Probability
0 0 10%
0 1 40%
1 0 30%
1 1 20%
1. Find the covariance.
The Graduate Management Admission Test (GMAT) has four sections: analytical writing, integrated reasoning, quantitative and verbal sections. Suppose that a researcher collected GMAT score data and calculated the covariance matrix across sections.
Analytical Writing Integrated Reasoning Quantitative Verbal
Analytical Writing 0.81
Integrated Reasoning 0.108 1.44
Quantitative 1.08 2.88 16
Verbal 0.54 1.8 4.8 9
Find the pair of two sections that have the largest correlation coefficient.
a. Quantitative and verbal
b. Analytical writing and quantitative
c. Analytical writing and integrated reasoning
d. Integrated reasoning and quantitative
e. Analytical writing and verbal
The following table gives the per-capital income in hundred dollars and the percentage of the economy represented by agriculture for some countries.
Per-capita Income ($100) 45 55 35 60 55
Percentage of the Economy in Agriculture (%) 9 8 4 8 6
Find the coefficient of correlation. (Use the sample variance and covariance formula.)