The proportion of the budget for a certain type of industrial company that is allotted to environmental and pollution control is coming under scrutiny. A data collection project determines that the distribution of these proportions is given by f(y) = 5(1−y)⁴, for 0 ≤ y ≤ 1, f(y) = 0, elsewhere.
(a) Verify that the above is a valid density function.
(b) What is the probability that a company chosen at random expends less than 10% of its budget on environmental and pollution controls?
(c) What is the probability that a company selected at random spends more than 50% of its budget on environmental and pollution controls?