Problem
The joint probability distribution of the size of a company's sales force (expressed in integer numbers) and its yearly sales revenue (expressed in million dollars) is shown in the table below. (This is an illustrative example: more detailed information would be better for real-life applications.)
Probability Sales Force Yearly Sales Revenues
0.10 15 1.53
0.20 20 1.06
0.25 25 2.61
0.25 30 3.85
0.20 35 4.03
I. Compute the mean, variance, and the standard deviation of the size of the sales force.
II. Compute the mean, variance, and the standard deviation of yearly sales revenue.
III. Compute the covariance and correlation of the size of the sales force and yearly sales revenue.
IV. Summarize in a sentence the result found in step (III).