Homework #7
Due Date: Friday December 4th at the start of class (Week 11)
There was no class in week 10, due to Thanksgiving.
Instructions: Download and unstuff the file HW7_YourName.zip to get up and running right away.
Exercise 1: ASCII ART
Run the file
Programming Homework #2: Calculations & Python Strings
Due Date: Friday October 16th 18th at 6PM. (Week 4)
Be able to demonstrate your working programs to a peer in class.
Exercise 0: Getting Started
i. Open
Programming Homework #5: More TKinter
Due Date: This Friday November 13th at the start of class. (Week 8)
Instructions: Download and unstuff the zipped file named HW5_YourName.zip
Be able to demonstrate your working programs in class on the due date.
E
Lecture 7a
ECE 361
Probability for Engineers
Fall, 2016
Steven Weber
Tuesday November 3, 2016
Steven Weber (Drexel ECE)
ECE 361 Fall 2016 Lecture 7a
November 3, 2016
1 / 41
3.5 Conditioning
Outline
1 3.5 Conditioning
Conditioning an RV on an event
Conditi
Steven Weber
Dept. of ECE
Drexel University
ECE 361 Probability for Engineers (Fall, 2016)
Lecture 8b (preliminary)
4.1 Derived distributions
Functions of two RVs
To find the PDF of Z = g(X, Y ) we use the same two step procedure: i) find the CDF FZ , ii)
Programming Homework #4: Using TKinter to create GUI programs
Due Date: This Friday November 6th at the start of class. (Week 7)
Instructions: Download and unstuff the zipped file named HW4_YourName.zip
Be able to demonstrate your working programs in clas
Programming Homework #3
Due Date: Friday October 23rd at the start of class. (Week 5)
Instructions: Import the zipped file named HW3_YourName.zip
Be able to demonstrate your working programs in class on the due date.
Exercise 1: Fibonacci numbers using
Homework #6
Due Date: Friday November 20th at the start of class (Week 9)
Instructions: Download and unstuff the file HW6_YourName.zip to get up and running right away.
Exercise 1: Cat Burglar and the Loyal Guard Dog
Run the file barking_dog.py
You should
Programming Homework #1: Introduction to Python
Due Date: Friday October 9th 18th at 6PM. (Week 3)
Be able to demonstrate your working programs to a peer in class.
Exercise 1: Print a custom greeting.
Y
Problem # 1:
ECE 361: Probability for Engineers HW # 5
Solution:
X is the current, the pdf of the current is
x2
x 2
f X ( x ) = 2 e 2b U ( x )
b
The power is
Y = X2
Since X is Rayleigh distributed, the power will be exponentially distributed as
y
1 2b2
e
ECE 361 HW # 2 Due July 11 in class
1. Five good fuses and two defectives ones are inadvertently mixed. To find the defective ones,
each one is tested one-byone. If the defective ones are identified only in the third attempt,
what is the probability of th
1. Solution:
ECE 361: Probability for Engineers HW # 8
August 22
f ( x, y=
) exp ( x y )U ( x )U ( y )
X
Z =X + Y W =
Y
This means that
=
x
z
x
J=
w
x
zw
x=
,
1+ w
z
y=
1+ w
zw
z
=
,y
1+ w
1+ w
z
1
y
=1
w
y
y
f ( z, w
=
)
1
2
1 + w)
(
x 1
x+ y
2 =
2 =
x
ECE 361: Probability for Engineers HW # 1 July 5 in class
1. The sample space of an experiment consists of the measured resistances of two resistors. Give
three examples of partitions.
Solution
Let R1 and R2 denote the measured resistances. The pair (R1,R
ECE 361: Probability for Engineers HW # 7 August 15
1.
Special case
X and Y identical
X and Y Rayleigh variables
Verification: Note that the range of w is 0<w<.
0
2w
(1 + w )
2 2
dw = 1
> int(2*w/(1+w^2)^2,w,0,inf) = 1
Note that Z=W+1. Therefore, the pdf
ECE 361: Probability for Engineers HW # 3 Due July 18
1. Test if the following expression is a valid probability density function and if it is, what is the
condition under which it will be valid?
g(x) =Be'f,x 2 0
Solution: 1=JIBe"2dx=x/;:>B=i
0
J;
2. Test
ECE 361: Probability for Engineers HW # 4 Due JULY 25
1. Find E[g(X)] , g(X ) = X 2 + 2 . X is exponentially distributed with a mean of 2.
Solution:
E[g(X)] =Ig(x)f(x)dx = [x2 +2]f(x)dx =Ix:f(.r)dx+'[2f(x)dx = E[X2]+2
f(x) =e 301x)
E(X)=2,var(X)=4=> (xl)=
ECE 361: Probability for Engineers HW # 9 due August 31
1.
Solution
=
f ( x)
Parallel connection:
1 5x
1 5y
=
e U ( x)
f ( y)
e U ( y)
5
5
The lifetime of the setup will be the maximum of the two
W=max(X,Y)
fW ( w ) 2 f x ( w ) F
=
=
X ( w)
w
2 w5
e 1
Problem 1
Problem 2
ECE 361: Probability for Engineers HW # 6 due August 8
Solution:
Z=2X+3Y = V + W
Mean(X)=5;
Var(X)=25;
Mean(V)=10; Mean(W)=15;
Var(V)=4*25=100, Var(W)=9*25=225
Problem 3
Solution:
xy
f ( x, y ) = 4 e
b
Verification: b = 5
x=raylrnd(5,
Practice Multiplier Problems:
Multiplier = (1 + C)/(rr + X + C)
Where:
rr = the required reserve ratio of reserves to deposits as mandated by the Fed
C = the ratio of cash held by the public to the deposits held by the public
X = the excess reserve ratio
Options Practice Worksheet
Compute the profits from the following positions and final stock prices.
1. Long Call X = 2.5
C=0.6
Stock Price = $3.4
answer= 0.3 = -0.6 + max(3.4-2.5,0)
2. Short Call X = 30
C=4.5
Stock Price = $35
answer=-0.5 = +4.5 - max(35-
YourLastName 1
YourFirstName YourLastName
Instructor's Name
Course Title
24 May 2017
Merger Assignment (Finance)
AT&T and Time Warner Merger
Qn 1.
This paper seeks to discuss the merger between AT&T and Time Warner as well as
answer some of the related qu
Chapter 6 Review Sheet
Entrepreneurship accepting the risk of starting and running a business
LO 6-1:
Reasons people are willing to take the entrepreneurship risk:
1.
2.
3.
4.
Opportunity
Profit you keep the profits of your company
Independence being your
Chapter 13 Review Sheet
LO 13-1:
Marketing The activity, set of institutions, and processes for creating, communicating,
delivering, and exchanging offerings that have value for customers, clients, partners, and society
at large
Marketing in the past was
Chapter 19 Review Sheet
LO 19-1:
Securities markets are financial marketplaces for stocks and bonds and serve two primary
functions:
Assist businesses in finding long-term funding to finance capital needs.
Provide private investors a place to buy and se