The first 4 pages contain the solution prepared without the use of Matlab. The remaining pages contain the solution as a
Matlab published file containing the Matlab code and the results (all obtained using the symbolic toolbox).
p m shankar, April 16, 201
Problem 19. Alice searches for her term paper in her ﬁling cabinet. which has several
drawers. She knows that she left her term paper in drawer j with probability p; > O.
The drawers are so messy that even if she correctly guesses that the term paper is i
1.4 Total Probability Theorem
and Bayes Rule
1
Total Probability Theorem
Let A1, A2, An be disjoint events that form a
partition of the sample space (each possible
outcome is included in exactly one of the events
A1, A2, An) and assume that P(Ai)>0, for a
2.4 Expectation & Variance
Recitation
Homework
2.5-2.6 PDF & CDF
Recitation
A ball is drawn from an urn containing 3 white and 3 black balls. After the ball is
drawn, it is then replaced and another ball is drawn. This goes on indefinitely.
What is the pr
Ece 361 w1 sec 1.3
1.3 Conditional Probability
What is Conditional Probability?
It provides a means to understand and
model the outcome of an experiment via
partial information
The conditional probability of event A
given event B is denoted by P(A|B)
Gene
Solution to Problem 1.20. Figure 1.1 provides a sequential description for the
three different strategies. Here we assume 1 point for a win, 0 for a. loss= and 1/2 point
Bold play
(a) (b)
Bold play
Bold play for a draw. In the case of a tied 1—1 score
2.4 Expectation & Variance
Recitation
2.5-2.6 PDF & CDF
Recitation
A ball is drawn from an urn containing 3 white and 3 black balls. After the ball is
drawn, it is then replaced and another ball is drawn. This goes on indefinitely.
What is the probability
1.
2.
ECE 361: Probability for Engineers HW # 5, due May 5
A current having a Rayleigh density is passed through a resistor of 2p Ohms. If the mean value of
the current is 2 A, (i) obtain an expression for the pdf of the power dissipated across the resist
ECE 361: Probability for Engineers HW # 1
1. A thermometer measures temperatures from -40 to 130oF. (a) Define the universal set for this
measurement (b) specify the subset for temperature measurements not exceeding waters
freezing point (c) specify the s
ECE 361: Probability for Engineers HW # 6, due May 12
1. The voltage X generated by a noise source is Gaussian N(0,9). This is passed through a square
law device with the output Y=5X2. (1) What is the density function of the output of the square
law devic
1.
ECE 361: Probability for Engineers HW # 4, due April 28
Find E[g(X)] with
g(X ) = X2
The density function of X is
1 x
f X ( x ) = e 2U ( x )
2
2. X is uniformly distributed [-5,15]. Find the mean of Y = e
3.
X
5
For the following density function,
?
x
ECE 361: Probability for Engineers HW # 1
1. A thermometer measures temperatures from -40 to 130oF. (a) Define the universal set for this
measurement (b) specify the subset for temperature measurements not exceeding waters
freezing point (c) specify the s
ECE 361: Probability for Engineers HW # 2
1. Two numbers x and Y are selected at random between 0 and 1. Three events are defined in
terms of the following outcomes: A=cfw_x>1/2; B=cfw_y>1/2 and C=cfw_x>y. Determine (a) if A and B
are independent (b) A an
1.
2.
3.
ECE 361: Probability for Engineers HW # 3, due April 21
Test if the following expression is a valid probability density function
= 3e x , x 0
g ( x)
Test if the following expression is a valid density function and if it is valid, determine the
co
Chapter 2 Discrete Random
Variables
1
2.1 What is a Discrete Random
Variable?
Consider an experiment that can have many outcomes
Let X represent all of the possible outcomes of the
experiment
Map all possible outcomes on the real number line
Each possibl
ECE 361: Probability for Engineers HW # 6, Soutions
1. The voltage X generated by a noise source is Gaussian N(0,9). This is passed through a square
law device with the output Y=5X2. (1) What is the density function of the output of the square
law device
ECE 361: Probability for Engineers HW # 2
1. Two numbers x and Y are selected at random between 0 and 1. Three events are defined in
terms of the following outcomes: A=cfw_x>1/2; B=cfw_y>1/2 and C=cfw_x>y. Determine (a) if A and B
are independent (b) A an
ECE 361: Probability for Engineers HW # 9
1. X and Y are continuous random variables with a density f ( x, y ) = x + y,
0 < x < 1, 0 < y < 1
Find the marginal density functions of X and Y. Are X and Y independent?
2. The received signal strengths (measure
ECE 361: Probability for Engineers HW # 7
1. X is a random variable with the following pdf:
1
, 1< x < 9
8
f (=
x)
Determine the pdf of Y =
1
.
X
Solution: The transformation is a monotonic one,
f (=
y)
f ( x) 1
1 1
= ( 2 x 3/2=
, < y <1
)
dy
8
4 y3 3
dx
1.
ECE 361: Probability for Engineers: HW # 3
Test if the following expression is a valid probability density function
=
g ( x ) 3e x , x 0
Solution
g ( x )dx 1
No.
0
2.
Test if the following expression is a valid density function determine the constant
Steven Weber
Dept. of ECE
Drexel University
ECE 361 Probability for Engineers (Fall, 2016)
Homework 3
Assigned:
Due:
Returned:
Thursday October 6, 2016
Thursday October 13, 2016
Monday October 17, 2016
(at the beginning of class 11am)
(in recitation)
Your
Steven Weber
Dept. of ECE
Drexel University
ECE 361 Probability for Engineers (Fall, 2016)
Lecture 3b
Some hints for homework 3
Hints on problems 1 and 8.
2.4 Expectation, mean, and variance
Mean and variance of some common RVs
Example. The mean and varia
Steven Weber
Dept. of ECE
Drexel University
ECE 361 Probability for Engineers (Fall, 2016)
Lecture 3a
2.3 Functions of random variables
Functions of RVs. A function of a RV X, say Y = g(X), is a new RV.
Example. Let X be the temperature in degrees Celsius
Steven Weber
Dept. of ECE
Drexel University
ECE 361 Probability for Engineers (Fall, 2016)
Lecture 2a
1.3 Conditional probability
Using conditional probability for modeling
Generalizing the arguments in the above example we identify the following multipli
Steven Weber
Dept. of ECE
Drexel University
ECE 361 Probability for Engineers (Fall, 2016)
Lecture 1a
1.1 Sets
A set S is an unordered collection of unique objects, called elements, with membership of element x in S denoted x S.
Empty (or null) set: .
Not