Boston University
Department of Electrical and Computer Engineering
EC505 STOCHASTIC PROCESSES
Problem Set No. 1 Solutions
Fall 2008 Issued: Wednesday, Sept. 3, 2008 Due: Friday, Sept. 12, 2008
Problem 1.1 A random experiment consists of tossing a die and
EC505
STOCHASTIC PROCESSES
Class Notes
c 2015 Prof. D. Castaon & Prof. W. Clem Karl
n
Dept. of Electrical and Computer Engineering
Boston University
College of Engineering
8 St. Marys Street
Boston, MA 02215
Fall 2015
2
Contents
1 Introduction to Probabil
EC381
Probability
(and a little Statistics)
Foundations of Probability
Dept. of Electrical and Computer Engineering
Center for Information and Systems Engineering
1.2 Axiomatic Theory of Probability
A. Concepts of Experiment, Outcome, Sample Space & Event
Boston University
Department of Electrical and Computer Engineering
EC505 STOCHASTIC PROCESSES
Notes on Finding Derived Distributions
c 2010 W. C. Karl
Consider the random experiment with the probability space (, F, P), where is the top right quadrant
of
Boston University
Department of Electrical and Computer Engineering
EC505 STOCHASTIC PROCESSES
Notes on Homework Formatting
c 2010 W. C. Karl
In these notes we discuss how you can help us give you the maximum amount of credit for your homework.
We ask tha
Stochastic Calculus
Stochastic Process: Random walk
Begins with a known value Xo at t = 0 then at t = 12.3 eitherjumps up
or down Le. 50% probability it will jump up or down. in the end we get a
cumulative sum of random variables.
Example: Simple Random W
Solution 5. (a) We clearly have Y0 = U. The function f (t, 1:) =: t%3 is in (72 and hence by
Its formula we get
6f 6f 1 a2 f
Y = _ _
d t at (t, Wth + axe, 14/1)th + 2 32$, mm [W, W]:
= 2th dt + 3:211? mm + $615211; d:
= (2th + 3t2Wt) cit + 3t2wf mm. (22)
Nomenclature
Random variables (X,Y) are known as
Bivariate random variable
Joint random variables (common experiment)
Random vector (of length 2)
Will generalize concepts from scalar random
variables to bivariate random variables first then
random ve