Gold Main Palette is a global coatings manufacturer based in New York City.The company has been making a steady income for some time selling house paint at Home Depot, Lowes, Ace, and other hardware stores."Everybody needs paint" says their CEO, Dave, who stresses the company's secure dependable profits at investor meetings.

Recently, Dave has been reflecting on the value of diversifying the company's profit flows.He is considering entry into the art supplies segment by launching an acrylic paint brand for arts & crafts.

We know the following about Dave's current monthly profits from house paint, X (in $millions):

E(X) = 140VAR(X) = 900

Based on the finance team's analysis, the company could add to their profits by serving the art supplies segment.The additional monthly profits from the art segment (in $millions), Y, would be such that:

E(Y) = 20VAR(Y) = 400

If Dave invests into this new segment, the company will earn total profits T = X + Y.

(a) Assume that profits from the two segments are independent.Calculate the expected value and variance of T.

(b) Assume instead that the correlation of monthly profits X and Y is 0.40.Calculate the variance of T.

(c) Now assume that we don't know the degree of correlation between the two profit flows.Define Q to be the covariance of X and Y.Find the range of values for Q such that investing in the new segment results in BOTH a higher expected value of total profits AND a lower variance in total profits compared to the current situation in which the only profit source is from house paint.