Introduction to Statistics Lecture 6
Estimation
October 16, 2014
1
Motivation
Statistical inference is concerned with making probabilistic statements about
unknown quantities.
Examples: means, variances, quantiles and unknown parameters of distributions.
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 comes from the specied distribution
or not.
1.1
The 2 -
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 examination. You can refer to two two-sided pages
of notes and th
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, independent
variable) and a response variable (output
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 2.1-2.3 of DeGroot and Schervish.
You may nd solutions to
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. You can refer to 2 two-sided pages
of notes.
3. Please
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 equally likely to be one of the 365
days of the year, indep
PROBABILITY & STATISTICAL INFERENCE
Department of Statistics, Columbia University
Autumn 2016
Instructor: Regina Dolgoarshinnykh
Oce: 1017 SSW (212-851-2150)
Email: [email protected]
Lecture Time: Mon and Wed 8:40am - 11:25pm, SSW903
Class Webpage:
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 population (base rate) is 0.5%. The test is highly accurate wi
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 behind every limit theorem lies a
probability inequality
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 credit for your solutions - correct answers without work wi
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 of 26
letters and a number is one among 0, 1, . . . ,
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).
1. (P9.1) (10 pts)
By Problem 1.4,
(1 B)d (A0 + A1 t
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 of 26
letters and a number is one among 0, 1, . . . ,
HW5 Solutions
5.8.2
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5.8.6
5.9.6
https:/www.coursehero.com/file/11299884/HW5Solutions/
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5.10.8
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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,
1.5.6,
1.5.12,
1.6.2,
1.6.6,
1.6.8,
1.7.2,
1.7.8,
1.7.10
HW8 Solutions
9.1.4
9.1.6
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9.1.8
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9.1.2
https:/www.coursehero.com/file/11299891/HW8Solutionsnew/
9.1.14
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9.1.16
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9.1.12
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HW 9 Solution
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11.1.2
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11.2.6
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11.2.12
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11.1.4
11.2.14
https:/www.cou
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,
1.5.6,
1.5.12,
1.6.2,
1.6.6,
1.6.8,
1.7.2,
1.7.8,
1.7.10
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: 2pm to 4pm Fridays in 1029 SSW (121 and
Amsterdam)
Textb
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 Review to Begin
Independent Random Variables
Independence i
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 / 59
The Exponential Distribution
Denition: A random vari
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
The probability distribution of a discrete random variabl
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. Suppose that X has a density given by f (x) = cx2 for
1 x 1
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 rolling two dice we are generally not interested in the se