Summary: Math 501. 5th Homework. Due Friday, November 16, 2007.
Homework on "Conditional Expectation".
1. Suppose that a test for diagnosing gonorrhea is positive with probability 0.95 for a
person with gonorrhea while it is positive with probability 0.01 for a person without
gonorrhea. The probability that a person has gonorrhea is 0.25. A person is tested
for the disease and the test indicates that he/she has it. Find the probability that
the person actually has the disease.
2. Let X and Y have the pdf
f(x, y) =
6(y - x) if 0 x y 1
(i) Find fY |X(y|x).
(ii) Find E[Y |X = x] and Var(Y |X = x).
3. An actuary models the lifetime in years of a random selected person as a r.v. X
with p.d.f. f(x) = 6x5
906 , for 0 < x < 90. For a 20year old, find:
(i) the probability that he lives above 70 years old.