Homework 0 Due  Jan 25, 2013 

1. A doctor has schedualed two appoitments, one at 1 p.m., the other at 1:30pm. 
The amount of time an appoitment last is independent exponential random variable 
with mean 30 min. Assuming both patients are on time, find the expected amount of 
time the 1:30pm appointment spend at the doctor's office.


2. Let X_1 and X_2 be two independent random variables with hazard function h_1(t) and h_2(t).

Show that P( X_1 < X_2 | min(X_1, X_2) = a ) = h_1(a) /( h_1(a) + h_2(a))

Generalize this to k random variables.



4. If X_1, X_2, X_3 are independent exponential random variables 
with rates lambda_1, lambda_2, lambda_3. Find
(a) P( X_1 < X_2 < X_3 )
(b) P( X_1 < X_2 | max(X_1,X_2,X_3) = X_3)