Conditional Probability Density

An individual whose level of exposure to a certain pathogen is x will contact the disease caused by this pathogen with probability P (x). (Regard x as a continuous variable.)

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, if P (x) is increasing in x, then the ratio of the conditional density in part

(a) to the conditional density in part (b) also increases in x.