The Fourier Domain
A complex study of complexity
Fourier Domain
Expresses an image as the sum of weighted sinusoids
Wavelengths are determined by image dimensions
Amplitudes are determined by sample v
EE 178
Probabilistic Systems Analysis
Autumn 2016 Tse
Lecture Note 13
Continuous Probability Continued
In Lecture 11, we introduced continuous random variables. For example, lets consider X Uni f [0,
EE 178
Probabilistic Systems Analysis
Autumn 2016 Tse
Lecture Note 12
Continuous random variables
Up to now we have focused exclusively on discrete random variables, which take on only a finite (or co
EE178: Probabilistic Systems Analysis, Autumn 2016
Homework 6
Due Wednesday , Nov 9, 5pm
1. Estimating Variance
You have available n samples X1 , X2 , . . . , Xn , drawn independently from a pmf pX .
HW1 Solutions
October 5, 2016
1.
(20 pts.) Random variables, sample space and events
Consider the random experiment of ipping a coin
1.
3.
ith
coin ip
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EE178 HW 8 Solutions
Nov 30, 2016
1.
(15 pts) Gaussian Distribution
If a set of grades on a probability examination in an inferior school (not Stanford!) are approximately Gaussian distributed with a
EE 178
Probabilistic Systems Analysis
Autumn 2016 Tse
Lecture Note 4
Conditional Probability Review
In the previous lecture, the conditional probability P(A|B) was defined as
summarizes the difference
EE178: Probabilistic Systems Analysis, Autumn 2016
Homework 1
Due Wed, Oct 5, in class
1. Random variables, sample space and events
Consider the random experiment of flipping a coin 4 times.
(a) Defin
EE 178
Probabilistic Systems Analysis
Autumn 2016 Tse
Lecture Note 15
Gaussian Distribution
The last continuous distribution we will look at, and by far the most prevalent in applications, is called t
HW4 Solutions
1. (20 pts.) Packets Over the Internet Again
n packets are sent over the Internet (n even). Consider the following probability models for the process:
(a) Each packet is routed over a di
EE 178
Probabilistic Systems Analysis
Autumn 2016 Tse
Lecture Note 18
Recap
In the general model of prediction, we have a model (with parameter ). We collect data to estimate the
parameters of the mod
HW5 Solutions
1. (50 pts.) Random homeworks again
(a) (8 pts.) Show that if two random variables X and Y are independent, then
E[XY ] = E[X]E[Y ]
Answer: Applying the definition of expectation we have
Plotting a Confidence Band Over a Scatterplot With Regression Line
Assume you have the data set named Data from Problem 1.19, with explanatory variable
named ACT and response variable named GPA. Assum
Addendum for Spring Quarter, 2014
Newly Added:
MEDICINE (MED) 120N | 3 UNITS |
Pathophysiology of Disease of the Heart
Preference to Freshmen. This course presents the anatomy and physiology of the he
An Introduction
to
Social Psychology
William McDougall, D.Sc., F.R.S.
Fellow of Corpus Christi College, and Reader in
Mental Philosophy in the University of Oxford
Fourteenth Edition with Three Supple
Confidence Intervals
Objectives:
Students should know how to calculate a standard error,
given a sample mean, standard deviation, and sample
size
Students should know what a confidence interval is, an
Lecture 6. Entropy of an Ideal Gas (Ch. 3)
Today we will achieve an important goal: well derive the equation(s) of state
for an ideal gas from the principles of statistical mechanics. We will follow t
A note on how well be evaluating your papers. Admittedly, grades on philosophical
essays are less objective than grades for physics problem sets, say (though, we
like to think, more objective than, fo
How many ways are there to pass through city A where the
arrows represent one-way streets?
Answer: mn ways
The counting principal: Suppose two experiments are to
be performed. If experiment 1 can re
Bayes' Rule
Bayes' Rule - Updating Probabilities
Let A1,.,Ak be a set of events that partition a sample space such that (mutually exclusive and exhaustive):
each set has known P(Ai) > 0 (each event
EE 178
Probabilistic Systems Analysis
Autumn 2016 Tse
Lecture 9
Some Important Distributions
There are four important distributions in probability: binomial, geometric, Poisson and Gaussian. We have
c
EE 178
Probabilistic Systems Analysis
Autumn 2016 Tse
Lecture Note 1
Introduction to Probability1
Life is full of uncertainty.
Probability is a framework to deal with uncertainty. Probability theory h
HW3 Solutions
1. (20 pts.) Packets Over the Internet
n packets are sent over the Internet (n even). Let Xi = 1 if the ith packet got lost and Xi = 0 otherwise.
Consider the following probability model
HW2 Solutions
1. (13 pts.) Colorful coins
(a) (3 pts.) Describe the basic random variables and the outcomes in the sample space, and give their
probabilities.
Answer: We have one random variable C whi
EE 178
Probabilistic Systems Analysis
Autumn 2016 Tse
Lecture 5
Independent random variables and building probability models
Just a recap, there are 3 steps in building a probability model of a real-w
EE178: Probabilistic Systems Analysis, Autumn 2016
Homework 4
Due Wednesday Oct 26, 5pm (Note new time.)
1. Packets Over the Internet Again
n packets are sent over the Internet (n even). Consider the
EE 178
Probabilistic Systems Analysis
Autumn 2016 Tse
Lecture Note 7
Examples of distributions continued
2 The homeworks of n students are collected in, randomly shuffled and returned to the students.
EE178: Probabilistic Systems Analysis, Autumn 2016
Homework 2 (Alternate)
Due Wed. Oct. 12 in class
1. Colorful coins
We are given three coins. The first coin is a fair coin painted blue on the heads