Solve the ff:

Beta Corporation is a mining business owned by Lee Hu Kay. As CEO of the firm, he confronts most of the problems concerning his employees and subsidiaries. Assist Lee Hu Kay in solving the following concerns in his company.

i. In one of his subsidiaries, Sheltron, gasoline is stocked in a bulk tank ead'l week. let X denote the proportion of the tank's capacity that is stocked in each week and let Y denote the proportion of the tank's capacity that is sold in the same week. Note that the gas station cannot sell more than what was stooked in each week, which implies that the value of Y cannot exoeed the value of X. A possible [olnt pdf of X and Yis given by EJIZXJ) = 3x, 0 S y S x SI. Using the method of transformation, find the probability density function of Z, the proportion of stock that remains unsold for the week. a. Using the method of transformation, find the probability density function of Z = i-X, the proportion of the tank's oapaclty that is not stocked in each week. b. What is the probability that more than 20% of the tank is not filled for the week