For Exercise 4.109, see page 220; for 4.110, see page 223; for 4.111 to 4.114, see page 228; for 4.115, see page 230; and for 4.116 to 4.118, see page 235.
4.117 Comparing sales.
It is unlikely that the daily sales of Tamara and Derek in the previous problem are uncorrelated. They will both sell more during the weekends, for example. Suppose that the correlation between their sales is . Now what are the mean and standard deviation of the difference ? Can you explain conceptually why positive correlation between two variables reduces the variability of the difference between them?
4.117
When two variables have a positive correlation, if one variable increases, the other will also increase. If one variable decreases, the other will also decrease. This results in the average differences being smaller than if they were independent. With independence, if one variable increases, the other could increase or decrease.