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, 0≤y ≤1@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?