The joint density of x and y is given by f ( x , y ) = { x e − ( x + y ) x > 0 , y > 0 0 otherwise are x and y independent? if, instead, f ( x , y ) were given by f ( x , y ) = { 2 0 < x < y , 0 < y < 1 0 otherwise would x and y be independent?

hi there!

the answer will be d: 2

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).