Carla is a statistician with a bank. She has collected debt-to-equity mix data on mature (M) and young (Y) companies. The debt percentages vary from 20% to 80% in her sample. Carla has defined D M as a variable for the mature companies from 0 to 1, with DM = 0 interpreted as the low of 20% debt and DM = 1.0 as the high of 80% debt. The variable for young corporation debt percentages DY is similarly defined. The probability distributions used to describe DM and DY are?

f(DM) = 3(1 – DM)2 0 ≤ DM ≤ 1

f(DY) = 2DY 0 ≤ DY ≤ 1

(a) Use different values of the debt percentage between 20% and 80% to calculate values for the probability distributions and then plot them.

(b) What can you comment about the probability that a mature company or a young company will have a low debt percentage? A high debt percentage?