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Families of Random Variables
Fall 2015
Instructor:
Ajit Rajwade
Topic Overview
We will study several useful families of random
variables that arise in interesting scenarios in statistics.
Discrete random variables- Bernoulli, Binomial,
Poisson, multinom
Assignment 1: CS 215
Due: 14th August before 11:55 pm
Remember the honor code while submitting this (and every other) assignment. All members of
the group should work on all parts of the assignment. We will adopt a zero-tolerance policy against
any violat
CHAPTER 3: SOME IMPORTANT DISTRIBUTIONS
3b - 0
Probability and Statistics
Kristel Van Steen, PhD2
Montefiore Institute - Systems and Modeling
GIGA - Bioinformatics
ULg
[email protected]
CHAPTER 3: SOME IMPORTANT DISTRIBUTIONS
CHAPTER 3: SOME IMPO
PLACEMENT OFFICE, IIT BOMBAY
INTERNSHIP POLICY (2015-2016)
The Internship process is coordinated by the Institute Placement Team consisting of the Professor-in- Charge
(PIC), Assistant Placement Officer (APO), other staff members at the Placement Office,
Table of Common Distributions
taken from Statistical Inference by Casella and Berger
Discrete Distrbutions
distribution
pmf
mean
variance
mgf/moment
Bernoulli(p)
px (1 p)1x ; x = 0, 1; p (0, 1)
p
p(1 p)
(1 p) + pet
Beta-binomial(n, , )
(+ )
(n ) ()( ) (x+
Sleep
Dreams
Hypnosis
SLEEP DISORDERS
INSOMNIA
1 IN 10 ADULTS RECURRING
PROBLEMS IN FALLING OR
STAYING ASLEEP
EXERCISE, AVOID CAFFEINE, AND
HAVE REGULATED SLEEP Helps
prevent insomnia
NARCOLEPSY
A SLEEP DISORDER
CHARACTERIZED BY
UNCONTROLLABLE SLEEP AT
BASIC PROBABILITY : HOMEWORK 2
Exercise 1: where does the Poisson distribution come from? (corrected)
Fix > 0. We denote by Xn has the Binomial distribution with parameters
n and /n. Then prove that for any k N we have
P [Xn = k ] P [Y = k ],
n
where Y ha
Assignment 2: CS 215
Due: 25th August before 11:55 pm
Remember the honor code while submitting this (and every other) assignment. All members of
the group should work on all parts of the assignment. We will adopt a zero-tolerance policy against
any violat
Families of Random Variables
Fall 2015
Instructor:
Ajit Rajwade
Topic Overview
We will study several useful families of random
variables that arise in interesting scenarios in statistics.
Discrete random variables- Bernoulli, Binomial,
Poisson, multinom
CECS 341
Homework#5
Computer Architecture
2015 R. W. Allison
Name _
SID _
Using this sheet as the cover sheet, submit solutions for these problems on separate sheets of paper (when necessary),
clearly showing all your wo
CS386ArtificialIntelligenceLab
18/08/2015,Tuesday
LabHandout5
_
GeneralInstructions
Create a folder named
YOURROLLNUM_lab5 ( e.g. 131050001_lab5) in
the home directory (or at a location of your choice). You need to submit a
compressed(tar.gzortgzonly)co
CS 215-Data Analysis and Interpretation
Mid-Semester Exam, 2 hrs
Instructions: Closed notes.
1. We have discussed in class, a closed form expression for w , the solution vector to multivariate
(linear) regression obtained by minimising the sum of squares
Skolemization, Most General Uniers,
First-Order Resolution
Torsten Hahmann
CSC 384, University of Toronto
March 07, 2011
Skolemization
Conversion of sentences FOL to CNF requires skolemization.
Skolemization: remove existential quantiers by introducing ne
Name_
Computer System Architecture
6.823 Final Examination
Name:_
This is an open book, open notes exam.
180 Minutes
21 Pages
Notes:
Not all questions are of equal difficulty, so look over the entire exam and
budget your time carefully.
Please wr
Lecture 3
Gaussian Probability Distribution
Introduction
l
l
Gaussian probability distribution is perhaps the most used distribution in all of science.
u also called bell shaped curve or normal distribution
Unlike the binomial and Poisson distribution, th
Computer System Architecture
6.823 Final Examination
Spring 2002
Name:_
This is an open book, open notes exam.
180 Minutes
22 Pages
Notes:
Not all questions are of equal difficulty, so look over the entire exam and
budget your time carefully.
Ple
C+ and the Perils of Double-Checked Locking
Scott Meyers and Andrei Alexandrescu
September 2004
Multithreading is just one damn thing after, before, or simultaneous
with another.
1
Introduction
Google the newsgroups or the web for the names of various de