PROBABILITY
Autumn 2016
Homework 1
Homework is due Wednesday, September 21 at 8:40am, EDT. You need to upload it to
courseworks assignments tab. Read Sections 1.1-1.10 and 2.1-2.3 of DeGroot and Scher
Introduction to Statistics Lecture 6
Estimation
October 16, 2014
1
Motivation
Statistical inference is concerned with making probabilistic statements about
unknown quantities.
Examples: means, varian
Nonparametrics
December 2, 2014
1
Tests of goodness-of-t
In some problems, before we collect data we have some specic distribution in mind for the
data we will observe. We can test if the data indeed
W4109: PROBABILITY & STATISTICAL INFERENCE
Fall 2014
Midterm
1. Please print your name and student ID number in the upper right corner of this page.
2. This is a closed book, closed-notes examination.
W4109: PROBABILITY & STATISTICAL INFERENCE
Autumn 2008
Midterm
1. Please print your name and student ID number in the upper right corner of this page.
2. This is a closed book, closed-notes examinatio
W4109: PROBABILITY & STATISTICAL INFERENCE
Autumn 2015
Homework 1
Homework is due Thursday, September 24 at 10:10am. You need to upload it to courseworks
assignments tab. Read Sections 1.1-1.10 and 2.
PROBABILITY & STATISTICAL INFERENCE
Department of Statistics, Columbia University
Autumn 2016
Instructor: Regina Dolgoarshinnykh
Oce: 1017 SSW (212-851-2150)
Email: [email protected]
Lecture Ti
Linear regression models
November 13, 2014
We are often interested in understanding the relationship between two or more variables.
Want to model a functional relationship between a predictor (input
October 38, 2014
Stat “T4109 Fall 2014 Midterm—II — Page 2 of 12
1. (10 points) (5 + 5) Let X1,. . .,Xn be 1m with p.d.f
9:6‘2 Hgm<oo,
0 otherwise,
ﬂack?) ={
Where 9 > U is the unknown parameter.
(a
Practice Midterm -1 Solutions Fall,2014
5. (15 points) Suppose a class has 30 students and let X be the number of distinct birthdays of
those students. Assume that the birthday of each student is equa
Introduction to Probability Lectures 9 & 10
October 9, 2014
In this lecture we introduce a number of approximation results.
1
Probability inequalities
There is an adage in probability that says that b
Stat W4109 Fall 2014
1.
‘ Solution:
Practice Final - Page 3 of 12 December 04, 2014
(10 points) Consider a routine screening test for a disease. Suppose the frequency of
the disease in the populat
Solution: Homework 9
Brockwell, P. J. & Davis, R. A. , Time series: theory and methods: 9.1, 9.2, 9.3, 9.4, 9.13 for
the three time series: Series B, C, and D (APPB.TSM, APPC.TSM, APPD.TSM in ITSM2000
Stat W4109
Fall 2015
Time Limit: 2.5 hours
Name (Print):
Student UNI:
Signature:
This exam contains 7 problems. Answer all of them. Point values are in parentheses. You must
show your work to get cred
Practice Problem Set
October 2, 2015
1
Problems
1. A California license plate consists of a sequence of seven symbols: number,
letter, letter, letter, number, number, number, where a letter is any one
Practice Problem Set
October 2, 2015
1
Problems
1. A California license plate consists of a sequence of seven symbols: number,
letter, letter, letter, number, number, number, where a letter is any one
HW5 Solutions
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5.9.6
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HW 9 Solution
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11.2.6
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11.2.12
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HW8 Solutions
9.1.4
9.1.6
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9.1.8
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9.1.14
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Dear Students,
The following problems from the book Probability and Statistics by DeGroot
and Schervish are due on Thursday September 17 (at the beginning of class):
Problem No.
1.4.4,
1.4.6,
1.5.4,
1
Statistics W4150: Introduction to Probability and
Statistics
Professor Philip Protter
1029 SSW; [email protected]; 212-851-2145
Lectures, Week 1
September 8 & 10, 2015
1 / 41
Details
Oce Hours: 2p
Statistics W4150: Introduction to Probability and
Statistics
Professor Philip Protter
1029 SSW; [email protected]; 212-851-2145
Lectures, Week 4
September 29 & October 1, 2015
1 / 46
A Bit of Revie
Statistics W4150: Introduction to Probability and
Statistics
Professor Philip Protter
1029 SSW; [email protected]; 212-851-2145
Lectures, Week 3, given by Gonzalo Mena
September 22 & 24, 2015
1 / 5
Statistics W4150: Introduction to Probability and
Statistics
Professor Philip Protter
1029 SSW; [email protected]; 212-851-2145
Lectures, Week 2
September 15 & 17, 2015
1 / 95
Very Short Review
Th
Homework #2 for STAT W4150
Professor Protter
September 17, 2015
Due: This homework is due on Tuesday, September 22, 2015, in class.
Please do the following exercises, showing all of your work.
1. Supp
Chapter 3
September 15, 2015
1
Random Variables
In many situations we are not concerned directly with the outcome of an experiment,
but instead with some function of the outcome.
For example, when rol