Continuous Random Variables
Krzysztof Herman
Syracuse University
September 21, 2016
Krzysztof Herman
Continuous Random Variables
Lecture's Outline
In this lecture we will:
dene the concept of a continuous random variable.
dene the concept of probability d
The Poisson Process
CIS 321
February 25, 2016
CIS 321
The Poisson Process
Poisson Process
We have already talked about this a bit.
CIS 321
The Poisson Process
Poisson Process
We have already talked about this a bit.
Today we will see how the poisson and g
The Law of Large Numbers
CIS 321
March 1, 2016
CIS 321
The Law of Large Numbers
Basic Idea
The bigger the sample or realization, the better the approximation
of the distribution.
CIS 321
The Law of Large Numbers
Basic Idea
The bigger the sample or realiza
More on Random Variables
CIS 321
February 2, 2016
CIS 321
More on Random Variables
Binomial Random Variable
Toss 10 coins at a time, the result is a 10tuple of heads and tails,
e.g. (H, T , H, T , T , T , T , H, T , H).
CIS 321
More on Random Variables
Bi
Covariance and Correlation
CIS 321
February 23, 2016
CIS 321
Covariance and Correlation
Joint distribution
I
Just the sensible defintion (i.e. exactly what you would
expect):
The joint probability mass function for discrete X , Y is
p(a, b) P(X = a, Y = b
Joint Distributions and Independence
CIS 321
February 11, 2016
CIS 321
Joint Distributions and Independence
Joint distribution
I
Now we have two sample spaces and we cross them: 1 2 .
CIS 321
Joint Distributions and Independence
Joint distribution
I
Now w
Conditional Probability and Independence
CIS 321
January 26, 2016
CIS 321
Conditional Probability and Independence
Review of last week
A probability function p on is a function p : P() [0, 1]
satisying two properties:
p() = 1
p(A B) = p(A) + p(B), when A
PROC. OF THE 13th PYTHON IN SCIENCE CONF. (SCIPY 2014)
1
Frequentism and Bayesianism: A Python-driven
Primer
Jake VanderPlas
arXiv:1411.5018v1 [astro-ph.IM] 18 Nov 2014
F
AbstractThis paper presents a brief, semi-technical comparison of the essential feat
JSS
Journal of Statistical Software
MMMMMM YYYY, Volume VV, Issue II.
http:/www.jstatsoft.org/
Tidy Data
Hadley Wickham
RStudio
Abstract
A huge amount of effort is spent cleaning data to get it ready for analysis, but there
has been little research on how
BULLETIN (New Series) OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 46, Number 2, April 2009, Pages 179205
S 0273-0979(08)01238-X
Article electronically published on November 20, 2008
THE MARKOV CHAIN MONTE CARLO REVOLUTION
PERSI DIACONIS
Abstract. The use
Simulation and Realizations
CIS 321
February 4, 2016
CIS 321
Simulation and Realizations
The Pattern So Far
I
We have been doing the same thing - plugging in outcomes,
getting probabilities.
CIS 321
Simulation and Realizations
The Pattern So Far
I
We have
Random Variables and Distributions
CIS 321
January 28, 2016
CIS 321
Random Variables and Distributions
Review Tuesday
We saw definitions for conditional probability, independence and
Bayes Theorem.
CIS 321
Random Variables and Distributions
Review Tuesday
Introduction, Outcomes, Events and Probability
CIS 321
January 21, 2016
CIS 321
Introduction, Outcomes, Events and Probability
Sets and Functions (easy stu)
A set is a collection of (abstract) objects, such as whole
numbers, but could be anything (schoolb
Simulation Example, Intro to Variance and
Expectation
CIS 321
February 9, 2016
CIS 321
Simulation Example, Intro to Variance and Expectation
Continuous Experiment: Single-server Queue
I
A water pump serves villagers - they line up for water.
CIS 321
Simul
Conditional Probability and Independence
Krzysztof Herman
Syracuse University
February 6, 2017
Krzysztof Herman
Conditional Probability and Independence
Lecture's Outline
In this lecture we will expand on the notion of probability and introduce the
instru
Numerical Summaries
Krzysztof Herman
Syracuse University
September 5, 2016
Krzysztof Herman
Numerical Summaries
Lecture's Outline
We will focus on numerical summary measures. We will consider measures of
centrality and dispersion together with their prope
Discrete Random Variables
Krzysztof Herman
Syracuse University
February 8, 2017
Krzysztof Herman
Discrete Random Variables
Lectures Outline
In this lecture we will:
define the concept of a random variable and make a distinction between
two types discrete
Expectation and Variance
Krzysztof Herman
Syracuse University
September 28, 2016
Krzysztof Herman
Expectation and Variance
Lecture's Outline
In this lecture we will expand on the notion of discrete and continuous random
variables. In the specic, we will d
Introduction and Overview
Krzysztof Herman
Syracuse University
August 18, 2016
Krzysztof Herman
Introduction and Overview
Lecture's Outline
In this rst class we will answer some key questions:
What is statistics and why is it important?
What is the dieren
Review, Outcomes, Events and Probability
Krzysztof Herman
Syracuse University
August 20, 2016
Krzysztof Herman
Review, Outcomes, Events and Probability
Lecture's Outline
In this lecture we will review the key mathematical notions necessary to
properly und
Graphical Summaries
Krzysztof Herman
Syracuse University
August 29, 2016
Krzysztof Herman
Graphical Summaries
Lecture's Outline
In the next two lectures we will study data summarization techniques.
Today we will focus on graphical summarization of both qu
Jennavie Pascual
Prof Herman
CIS321 M001
23 February 2017
Homework Assignment #3
1. (4.7)
a. X has a Bin(1000, 0.001) distribution. Xi = 1 if the ith lamp is defective, otherwise its equal to
0, for i = 1, 2, 3, 1000.
b. The probability of no defective la
Jennavie Pascual
Prof Herman
CIS 321 M001
16 February 2017
Homework #2
0. 3.14
a. P(W|R) means that given the prize is behind the initially-chosen door, youll win by switching
doors. The probability of this would be 0, or P(W|R) = 0.
P(W|Rc) means that gi
Exam 1 sample problems, CIS 321
We have covered the rst 9 chapters of the text A Modern Introduction to
Probability and Statistics: Understanding Why and How, excluding Chapter
8. You should know all of the concepts explained there. Below you will nd
some
The Central Limit Theorem
CIS 321
March 3, 2016
CIS 321
The Central Limit Theorem
A Refinement of LLN
The LLN tells us about central tendency of sample averages.
CIS 321
The Central Limit Theorem
A Refinement of LLN
The LLN tells us about central tendency