University of Massachusetts - Amherst
Department of Electrical and Computer Engineering
ECE 314 Introduction to Probability and Random Processes
Spring 2016 Syllabus
DESCRIPTION
This course provides an elementary introduction to probability and statistics
Name:
ID:
ECE 314 - Introduction to Probability and Random Processes, Spring 2012
Quiz #3
In class: 02/15/2012
Exercise 1. A box containing 8 red, 3 white, 9 blue balls. If 3 balls are drawn at random without replacement determine the probability
(a) that
HW 10 Solutions
ECE 314 Introduction to Probability and Random Processes Spring 2013
May 1, 2013
Problem 1
First we need to nd ( 2 ).
2
Since we want 95% condence, 1 = .95, so = .05.
2
= .975. Using z-function table, (.975) = 1.96.
2
Now you can solve for
HW 9 Solutions
ECE 314 Introduction to Probability and Random Processes Spring 2013
April 23, 2013
Problem 1
(a)
We can easily nd the piecewise constant density of Y
1 , |y | 1
4
1
fY (y ) = 8 , 1 < |y | 3
0, otherwise
The conditional probabilities of X
HW 8 Solutions
ECE 314 Introduction to Probability and Random Processes Spring 2013
April 17, 2013
Problem 1
We can write the joint pdf for X and Y jointly Gaussian as:
fX,Y (x, y ) =
exp([a(x x )2 + b(y Y )2 + c(x x )(y Y )])
2X Y
where a =
1
2,
2(12 )X
HW 6 Solutions
ECE 314 Introduction to Probability and Random Processes Spring 2013
March 29, 2013
Problem 1
We have for x 0:
P (X > x|A) = P (T > t + x|T > t) =
=
P (T > t + x and T > t)
P (T > t)
e(t+x)
P ( T > t + x)
=
= ex
t
P (T > t )
e
Problem 2
If
HW 5 Solutions
ECE 314 Introduction to Probability and Random Processes Spring 2013
March 12, 2013
Problem 1
(a)
Legitimate PMF because
1
X
k=0
k
e
k!
2
=e
(1 +
+
2!
3
+
3!
+ ) = e
e =1
(b)
E [X ] =
=
=
=
1
X
k=0
1
X
k
ke
k
ke
k=1
1
X
k=1
1
X
m=0
=
k!
k!
HW 4 Solutions
ECE 314 Introduction to Probability and Random Processes Spring 2013
March 7 , 2013
Problem 1
To verify this rule, we let Y = g (x) and use the formula
pY ( y ) =
pX (x)
cfw_x|g (x)=y
E [g (x)] = E [Y ]
=
ypY (y )
y
=
y
y
pX (x)
cfw_x|g (x
Solutions homework 3
Problem 1
We break this into two parts.
The first part we look at is that the 15th flip is the 10th head. That means that the
15th flip is a head (this occurs with probability p) and 9 of the first 14 flips were
heads. Since flipping
HW 7 Solutions
ECE 314 Introduction to Probability and Random Processes Spring 2013
April 9, 2013
Problem 1
(a)
Region where fX,Y (x, y )is non-zero.
f X ( x) =
Z1
fX,Y (x, y )dy
1
81 x
< R 3(x + y )dy = 3x(1
=
:0
0,
fY (y ) =
x) + 3 y 2
2
1x
0
=
3
2
32
x
Department of Electrical and Computer Engineering
University of Massachusetts, Amherst
ECE 314: Introduction to Probability and Random Processes
Spring 2011
Course Webiste:
Course offered on SPARK.
Instructors:
Prof. Hossein Pishro-Nik
215I Marcus Hall
Ph
Tong Huang ECE314 spring 2997 Homework 4
0.3 y 0 0.05 y 1 0.15 y 2 1. a) PY (y) 0.1 y 3 0.4 y 4 0 otherwise b) According to the CDF given, 35% of students score 1 or less, and 50% of students score 2 or less. We have to made the passing probability
Tong Huang ECE314 Spring 2007 Assignment 3 1. a) Assume drawing cards without replacements. The probability of drawing all 4 4 3 2 1 24 3.693785 *10 6 . aces with 4 cards is * * * 52 51 50 49 6497400 We are drawing 5 cards, therefore there are 5 choo
Tong Huang ECE 314 spring 2007 Homework 2 1. Given P(A) 0.3; P(B) 0.6; P(C) 0.2; P(A C) 0; P(B | C) 0.5;P(A B C) 0.8. a) Because P(A C) 0 , which means A and C are independent events, so the intersection of A, B and C must be 0. b) P(B | C) P(BC) / P