1. When a patient is screened for the presence of a disease in an organ, a section of tissue isviewed under a microscope and a count of abnormal cells is made. Even under healthy conditions, a small number of abnormal cells will be present. Presumably a much larger number will be present if the organ is diseased. Assume that the number L of abnormal cells in a section is geometrically distributed.

Pr[L=l](1-a)a^l , l=0,1,...

The parameter-of a diseased organ will be larger than that of a healthy one. Therefore, we

have the following hypothesis test:

H0:Pr[L=l](1-a0)a0l, l=0,1,...

H₁:Pr[L=l](1-a₁) a₁^l, l=0,1,...

where ₁ > ₀ are known. The probability of a randomly selected organ being diseased is p.

A) Find the Bayes rule for deciding whether an organ is diseased.

B) What is the probability of correctly diagnosing a diseased organ?