Homework 4 Due April 5, 2013 


1. problem 23 (c) on page 278 of Ross book (10th Ed). 

2. (Same question as in the test):  N(t) a Poisson process with intensity lambda,

   and 0 < s < t < r  are given real numbers.

   Show that  E[ N(t)N(r) | N(s)] = [N(s)]^2 + lambda N(s)[ t-s + r-s ] + lambda^2 (t-s)(r-s) + lambda (t-s)
 




Recall:  Conditional expectation rules: (1) for any random variable X, we have  E[X|X] = X .
                (2) If X and Y are independent, then E[X|Y] = E[X].