HW6
===

(1) pb 10 p.265
  Do not attempt the last part of the question.


(2) pb. 3 p. 274
Set up the equation (we did a similar calculation in class), but do not solve it. 


(3) Consider a BDP with absorbing barrier at 0. In class we calculated the 
  probability of absorption, given that the process starts at i: 
    alpha_i = P(absorption | N(0)=i)

  Assume that the process gets absorbed for sure (i.e. when \sum \rho_i = infinity),
  and denote by W_i the time to absorption, starting from N(0)=i, that is
  W_i = E( T | N(0)=i)

  Set up a 2nd order difference equation for W_i using a first step analysis, and 
  specify the boundary condition(s). The resulting equation should be non-homogeneous
  with non-constant coefficients.
  Do not solve this equation (it is possible but not friendly), but write down in 2 
  or 3 lines how you would proceed.


(4) Consider a simple BD process with absorbing barrier at 0. "Simple" means
   lambda_n = n.lambda and mu_n = n.mu, lambda > 0, mu > 0.

   Determine the probability of absorption at 0 given that the process starts at N(0)=i.
   Verify that this probability tends to 0 as i tends to infinity, under condition(s) you
   should specify.

   Under what condition(s) is absorption certain? Does it make sense?


(5) 6.9.8

(6) 6.9.12

(7) 6.11.2



THIS IS COMPLETE