Course No. Stat 433
April 28, 2009
Homework 13 Solution
Page 497 Question 2.4
Let z be the hitting time of z .
P (M (t) z, B (t) x)
= P (z t, B (t) x)
= P (z x, z (B (t) z ) x)
= P (z x, B (t) 2z x)
= P (B (t) 2z x)
2z x
= 1 ( )
t
Differential with respec
Course No. Stat 433
April 28, 2009
Homework 11 Solution
Comments from the grader:
These are only partial solutions. We selected questions which were problematic to most of the class or are of particular interest.
The maximum grade for this homework assi
Course No. Stat 433
April 28, 2009
Homework 11 Solution
Comments from the grader:
These are only partial solutions. We selected questions which were problematic to most of the class or are of particular interest.
The maximum grade for this homework assi
Course No. Stat 433
April 28, 2009
Homework 10 Solution
Comments from the grader:
These are only partial solutions. We selected questions which were problematic to most of the class or are of particular interest.
The maximum grade for this homework assi
Course No. Stat 433
April 28, 2009
Homework 9 Solution
Comments from the grader:
These are only partial solutions. We selected questions which were problematic to most of the class or are of particular interest.
The maximum grade for this homework assig
Course No. Stat 433
April 28, 2009
Homework 8 Solution
Comments from the grader:
These are only partial solutions. We selected questions which were problematic to most of the class or are of particular interest.
The maximum grade for this homework assig
Course No. Stat 433
April 28, 2009
Homework 7 Solution
Comments from the grader:
These are only partial solutions. We selected questions which were problematic to most of the class.
The maximum grade for this homework assignment is 10.
Your solution sh
Course No. Stat 433
April 28, 2009
Homework 4 Solution
Comments from the grader:
These are only partial solutions. We selected questions which were problematic to most of the class.
The maximum grade for this homework assignment is 10.
Your solution sh
Course No. Stat 433
April 28, 2009
Homework 3 Solution
Comments from the grader:
These are only partial solutions. We selected questions which were problematic to most of the class.
The maximum grade for this homework assignment is 10. The points are
NO
Course No. Stat 433
April 28, 2009
Solution Homework 2
Comments from the grader:
These are only partial solutions. We selected questions which were problematic to most of the class.
The maximum grade for this homework assignment is 10.
Your solution sh
Course No. Stat 433
April 28, 2009
Homework 1 Solution
Comments from the grader:
These are only partial solutions. We selected questions which were problematic to most of the class.
The maximum grade for this homework assignment is 10.
Your solution sh
STAT 433: FINAL EXAM SOLUTIONS
QUESTION 1
(a) Transient states cfw_1
(b) Periodic states cfw_3, 5
(c) Communicating classes cfw_2, 4 and cfw_3, 5
(d) 2 = 4 = 1/2
QUESTION 2
(a)
E [M (t)]
0
E [f (t)]
= E [N (t) f (t)]
= E [X (t)2 + Y (t)2 + Z (t)2 ] E [f (