Math 230 Section 4 Quiz #4
1. A bacteria culture grows with a constant relative growth rate. After 2 hours there are 600
bacteria and after 8 hours the count is 75,000. Find the initial population.
Use P (t) = P (0)ekt , where P (t) is the population afte
Lecture 16: Expected value, variance, independence
and Chebyshev inequality
Expected value, variance, and Chebyshev inequality. If X is a random variable
recall that the expected value of X, E[X] is the average value of X
Expected value of X :
E[X] =
X
P
Graph Mining Class Notes
Amin Assareh
Probability
Definition 1: Probability Space ( , F, P)
=Sample space: all possible results
Example: roll a six sided die, results is =cfw_1 2 3 4 5 6
F - power set of : set of all possible subsets.
|F | = 2|
P - pro
13
Joint Distributions of Discrete Random
Variables
Sometimes it is useful to consider more than one random variable at the
same time, or to write a random variable as a combination of other random
variables. In this section we develop some of this theory
582691 Randomized Algorithms I
Spring 2013, period III
Jyrki Kivinen
1
Position of the course in the studies
4 credits
advanced course (syvent
av
at opinnot) in algorithms and machine
learning
prerequisites: basic understanding of probabilities and des
Chapter 2
Linearity of Expectation
Linearity of expectation basically says that the expected value of a sum of random variables
is equal to the sum of the individual expectations. Its importance can hardly be overestimated for the area of randomized algor
A Primer on Inequalities
Introduction: Basic Inequalities
When working in the set of real numbers, we have a law of trichotomy. Given x, y R exactly one of these is
true: x < y, y < x, or x = y. This (almost) defining characteristic of the real line means
Chapter 2
Famous Inequalities
I speak not as desiring more, but rather wishing a more strict
restraint.
Isabella, in Measure for Measure, by William Shakespeare
In this chapter we meet three very important inequalities: Bernoullis Inequality, the
Arithmet
San Jose State University
SJSU ScholarWorks
Master's Theses
Master's Theses and Graduate Research
2013
Mathematical Inequalities
Amy Dreiling
San Jose State University
Follow this and additional works at: http:/scholarworks.sjsu.edu/etd_theses
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5MD20Design Automation
Randomized Algorithms and Probabilistic
Analysis of Algorithms
Phillip Stanley-Marbell
TU/e 5MD20
Lecture: Randomized Algorithms
1
Lecture Outline
Motivation
Probability Theory Refresher
Example Randomized Algorithm and Analysis
Fall 2009 version of Course 15-359,
Computer Science Department,
Carnegie Mellon University.
Acknowledgments:
CMUs course 15-359, Probability and Computing, was originally conceived and
designed by Mor Harchol-Balter and John Lafferty. The choice, order,
Probability and Computing
Randomized Algorithms and Probabilistic Analysis
.
.
\
'.
'.
Michael Mitzenmacher
Eli Upfal
Probability and Computing
Randomization and probabilistic techniques play an important role in modern computer science, with applications
ST2334: SOME NOTES ON THE GEOMETRIC AND NEGATIVE
BINOMIAL DISTRIBUTIONS AND MOMENT GENERATING
FUNCTIONS
Geometric Distribution
Consider a sequence of independent and identical Bernoulli trials with success
probability p (0, 1). Define the random variable
MOMENT-GENERATING FUNCTIONS
1. Demonstrate how the moments of a random variable x may be obtained
from its moment generating function by showing that the rth derivative of
E(ext ) with respect to t gives the value ofr )E(x
at the point where t =0.
Show th
Geometry of Complex Numbers
1 of 9
about:reader?url=http:/mathfaculty.fullerton.edu/mathews/c2003/Com.
mathfaculty.fullerton.edu
Geometry of Complex Numbers
Module
for
Geometry of Complex Numbers
1.3 The Geometry of Complex Numbers
Complex numbers are ord
Shiv Nadar University
MAT-101
Assignment -1
Due Date - 12/09/2014 3 p.m
1. (a) State the definition of
i. Upper bound and lower bound of a set
ii. Bounded set
iii. Maximum and Supremum of a set.
(b) Give example of
i.
ii.
iii.
iv.
v.
(c)
A
A
A
A
A
set whi
Notes on Randomized Algorithms
CPSC 469/569: Fall 2016
James Aspnes
2016-12-19 14:34
Contents
Table of contents
i
List of figures
xii
List of tables
xiii
List of algorithms
xiv
Preface
xv
Syllabus
xvi
Lecture schedule
xix
1 Randomized algorithms
1.1 A tri