January 19
Biases
1. We make a mistake representing units that are not representative of our population. (ex.
Blood pressure reduction medicine, but somehow only give it to men in this experiment.
Then we cant generalize the results to both men & women. S
Aliza Seidenfeld
STAT 111-201
February 9, 2016
Homework 2
1.
a) Scatterplot of Nondominant and Dominant arm strength
b) The pattern in this scatterplot shows that as the strength in the bones of the Nondominant
arm increases, so does the strength in the b
Aliza Seidenfeld
STAT 111 201
March 6, 2016
Homework 4
1. IPS Exercise 5.20, p. 318 [Facebook]
= 190 friends
Median = 100 friends
= 288
SRS = 70 Facebook users
a) For your sample, what are the mean and standard deviation of X (barred), the mean
number o
Aliza Seidenfeld
STAT 111-201
February 3, 2016
Homework 1
1. a) In this survey the population is 5,764 season ticker holders at college football games.
b) The sample is 98 fans out of the 5,764 fans who were sent the survey.
c) The response rate is 98/150
Bias in experiment: 1. Not rep of pop 2. Lurking/confounding in treatment vs control. 3. Subjects
know in experiment 4. Evaluators know. W/ confounding, conclude association. Matching,
randomization, or both! (randomized math pairs, randomized blocks) Obs
STAT Recitation
January 29, 2016
- First thing we do is import data.
- Need to save anything in same folder as directory R is getting documents from.
- Miscellaneous on top and go to change working directory and choose which one you
want
- Survey.data=3.c
Chapter 4
Some Counting Problems;
Multinomial Coecients, The
Inclusion-Exclusion Principle,
Sylvesters Formula, The Sieve
Formula
4.1
Counting Permutations and Functions
In this short section, we consider some simple counting
problems.
Let us begin with p
Example 2c of Sheldon Ross
Somabha Mukherjee
02-03-2017
Question: In the card game bridge, the 52 cards are dealt out equally to 4 players-called East,
West, North, and South. If North and South have a total of 8 spades among them, what is the
probability
Practice Problems
The exam will be closed book, without any notes. No calculators. Full credit will only be given for complete, clear and
accurate answers.
1. Let A, B and C be three events.
Define what it means for A, B and C to be independent.
2. Let S
Statistics 430 Midterm 2 Information, Spring 2014
Exam will be closed book, without any notes. The topics listed below form the core focus of the exam.
1
Topics
1. probability mass function.
2. Definition of mean and variance as well as computation of Eg(
Practice Problems Stat 430
1. Let X and Y be independent random variables. Suppose that EX = 1, EY = 0, V ar(X) = 10, V ar(Y ) = 9. Find
E(3X 2Y )2 .
2. Let X and Y be independent random variables. Suppose that EX = 1, EY = 0, EX 2 = 12, EY 2 = 12. Find
V
. -.RELATION BETWEEN POISSON AND MULTINOMIAL DISTRIBUTIONS
Robert G.D. Steel
Introduction.
April, 1953
BU-39-M
It is usual to see the Poisson distribution developed
from the binomial distribution by removing the restriction on the exponent.
Here it is sho
Chapter 2
Distributions of Order Statistics
We give some important formulae for distributions of order statistics. For example,
Fk:n (x) = Pcfw_Xk,n x = IF(x) (k, n k + 1),
where
Ix (a, b) =
1
B(a, b)
x
0
t a1 (1 t)b1dt
denotes the incomplete Beta functi
TARTU UNIVERSITY
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE
Institute of Mathematical Statistics
Frazier Carsten
Overdispersed Models for Claim
Count Distribution
Masters Thesis
Supervisor: Meelis Kaarik, Ph.D
TARTU 2013
Contents
1 Introduction
3
2 Class
2WB05 Simulation
Lecture 8: Generating
random variables
Marko Boon
http:/www.win.tue.nl/courses/2WB05
January 7, 2013
Outline
1. How do we generate random variables?
2. Fitting distributions
Department of Mathematics and Computer Science
2/36
Generating r
28CHAPTER 2. EFFICIENCY AND THE CRAMER-RAO
INEQUALITY
2.
Iij () = Cov (Si (X) , Sj (X)
i, j = 1, 2, . . . , k
(2.24)
Example Let X1 , X2 , . . . , Xn be a random sample from the N (, 2 ) distribution. Find the CRLB and, in cases 1. and 2. check whether i
(b) Let X U (0, 40). We want to find P (X > 30|X > 10). By Bayes Rule,
P (X > 30|X > 10) =
=
=
=
=
P (X > 30)
P (X > 10)
R 40 1
40 dx
R30
40 1
10 40 dx
x]40
30
x]40
10
40 30
40 10
1
3
40. If X is uniformly distributed over (0, 1), find the density functio
Stat 613
Class 10
Richard P. Waterman
Wharton
August 16, 2015
August 16, 2015
1 / 17
Table of contents I
1
What you need to know from last time
2
Todays material
3
Log transforms and their interpretations
4
Simple Logistic Regression. Chapter 11
5
Review
Stat 613
Class 5
Richard P. Waterman
Wharton
August 16, 2015
August 16, 2015
1 / 15
Table of contents I
1
What you need to know from last time
2
Todays material
3
Fitting equations to data
Why fit?
Least squares
Interpretation
4
Regression diagnostics
Ass
Stat 613
Class 7
Richard P. Waterman
Wharton
August 16, 2015
August 16, 2015
1 / 19
Table of contents I
1
What you need to know from last time
2
Todays material
3
Outliers, p.61
4
Understanding almost all the regression output
5
Confidence interval for th
Stat 613
Class 3
Richard P. Waterman
Wharton
August 16, 2015
August 16, 2015
1 / 25
Table of contents I
1
What you need to know from last time
2
Todays material
3
Sampling
Introduction
Issues in sampling
The Utopian sample for analysis
Precision considera
Stat 613
Class 8
Richard P. Waterman
Wharton
August 16, 2015
August 16, 2015
1 / 24
Table of contents I
1
What you need to know from last time
2
Todays material
3
Collinearity
4
Hypothesis testing in multiple regression
5
Categorical variables as predicto
Stat 613
Class 4
Richard P. Waterman
Wharton
August 16, 2015
August 16, 2015
1 / 23
Table of contents I
1
What you need to know from last time
2
Todays material
3
Hypothesis tests on means
The p-value
4
Comparative analytics
Two sample t-tests
The Wilcoxo
Stat 613
Class 1
Richard P. Waterman
Wharton
August 16, 2015
August 16, 2015
1 / 39
Table of contents I
1
2
3
4
5
6
Introduction
The course rationale
Quick review of the syllabus
Course overview
Todays material
Chapter 2 in BBS
Statistical graphics and su
Stat 613
Class 9
Richard P. Waterman
Wharton
August 16, 2015
August 16, 2015
1 / 30
Table of contents I
1
What you need to know from last time
2
Todays material
3
Categorical variables as predictors (two groups)
4
The model hierarchy
5
Interaction in regr
Stat 613
Class 2
Richard P. Waterman
Wharton
August 16, 2015
August 16, 2015
1 / 30
Table of contents I
1
What you need to know from last time
2
Todays material
3
Monitoring the mean and variance of a process
4
An example to get intuition for the SE mean
Stat 613
Class 6
Richard P. Waterman
Wharton
August 16, 2015
August 16, 2015
1 / 14
Table of contents I
1
What you need to know from last time
2
Todays material
3
Regression diagnostics
Outliers, p.61
4
Understanding almost all the regression output
5
Con
-title: "Lecture 8: Probabilities and Simulation"
author: Robert Stine, Stat 405/471
date: Spring 2017
output: html_notebook
-R provides a wide range of functions for generating random values, as well as
accompanying functions that compute probabilities a