20. An individual whose level of exposure to a certain pathogen is x will contract the disease caused by this pathogen with probability P(x). If the exposure level of a randomly chosen member of the population has probability density function f , determine the conditional probability density of the exposure level of that member given that he or she

(a) has the disease.

(b) does not have the disease.

(c) Show that when P(x) increases in x, then the ratio of the density of part (a)

to that of part

(b) also increases in x.