Frequencies and barplots
Summary statistics. The main summary statistics are the frequencies or counts (aka frequencies) for each of
the six digits:
Ns = #cfw_i : Xi = s,
s = 1, . . . , 6
When the trials are assumed independent, these counts are jointly s
The chi-squared distribution
Let m be a positive integer, and suppose Z1 , . . . , Zm are i.i.d. standard normal. Then the variable
2
Y = Z12 + + Zm
is said to have the chi-squared distribution with m degrees of freedom.
It has density:
f (x) =
1
xm/21 ex
In general, suppose we observe an i.i.d. sample from a discrete distribution X1 , . . . , Xn cfw_a1 , . . . , aS , with
P (Xi = as ) = ps ,
s = 1, . . . , S
The parameters p1 , . . . , pS define the underlying distribution and, in the context of statisti
17 / 25
In our example, the probability of the observed table is
8
4 4
/
4
3 1
There is only one more extreme table
Milk
Tea
Sum
Milk
4
0
4
Tea Sum
0
4
4
4
4
8
and it has probability
8
4 4
/
4
4 0
The p-value is the sum of these:
8
4 4
8
4 4
0.2429
One-Sample Categorical Data
University of California, San Diego
Instructor: Ery Arias-Castro
http:/math.ucsd.edu/~ eariasca/teaching.html
1 / 11
Testing the fairness of a die
A casino is inspected. The undercover inspector tests the fairness of a 6-face d
Winter 2015
Math 20B
Exam 1 vA
University of California, San Diego
Department of Mathematics
Instructions
1. Write your Name, PID, Section, and Exam Version on the front of your Blue Book.
2. No calculators or other electronic devices are allowed during t
Winter 2016
Math 20B
Exam 1 vA
University of California, San Diego
Department of Mathematics
Instructions
1. Write your Name, PID, Section, and Exam Version on the front of your Blue Book.
2. No calculators or other electronic devices are allowed during t
Math 20A-C; Topics & Textbook
If you choose to retake these courses (IF YOU ALREADY GOT CREDIT FOR EM KIDDOS
THROUGH AP), you would be wasting approximately $1,200 per course; thats your business
not mine. (youll take about 10 classes a year, or about 14
Lecture Notes for Math20B on Nov 21, 2014
Announcement
Review classes
Wednesday in class:
Today in class:
S.1, S.2, S.3, 7.1, 7.3
10.1, 10.2, 10.3 (10.3 wont be in midterm )
Friday by Zev Finnley
5:00-5:50pm, @ CSB 02.
Sunday by Michelle Bodnar
3:0
Math 20B Supplement
January 2012 version
Linked to Calculus: Early Transcendentals, by Jon Rogawski, Edition 2, c 2012
Written by
Ed Bender, Bill Helton and John Eggers
Contributions by
Magdelana Musat and Al Shenk
Maintenance Crew
Bill Helton, John Egger
Math 20B Supplement
January 2012 version
Linked to Calculus: Early Transcendentals, by Jon Rogawski, Edition 2, c 2012
Written by
Ed Bender, Bill Helton and John Eggers
Contributions by
Magdelana Musat and Al Shenk
Maintenance Crew
Bill Helton, John Egger
Name:
TA:
PID:
Sec. No:
Sec. Time:
Math 20B.
Final Examination
June 11, 2010
Turn o and put away your cell phone.
No calculators or any other devices are allowed on this exam.
You may use one page of notes, but no books or other assistance on this exam.
R
Name:
Section Number:
TA Name:
Section Time:
Math 20B.
Midterm Exam 2
May 17, 2010
Turn o and put away your cell phone.
No calculators or any other devices are allowed on this exam.
You may use one page of notes, but no books or other assistance on this e
Name:
TA:
PID:
Sec. No:
Sec. Time:
Math 20B.
Midterm Exam 1
April 19, 2010
Turn o and put away your cell phone.
No calculators or any other devices are allowed on this exam.
You may use one page of notes, but no books or other assistance on this exam.
Rea
Winter 2013
Math 20B
Exam 2 vA
University of California, San Diego
Department of Mathematics
Instructions
1. Write your Name, PID, Section, and Exam Version on the front of your Blue Book.
2. No calculators or other electronic devices are allowed during t
Winter 2013
Math 20B
Exam 1 vA
University of California, San Diego
Department of Mathematics
Instructions
1. Write your Name, PID, Section, and Exam Version on the front of your Blue Book.
2. No calculators or other electronic devices are allowed during t
Fall 2012
Math 20B
Final Exam vA
University of California, San Diego
Department of Mathematics
Instructions
(a) Write your Name, PID, Section, and the Version of your exam on the front of your Blue Book.
(b) No calculators or other electronic devices are
Fall 2012
Math 20B
Exam 2 vA
University of California, San Diego
Department of Mathematics
Instructions
1. Write your Name, PID, Section, and the Version of your exam on the front of your Blue Book.
2. No calculators or other electronic devices are allowe
Fall 2012
Math 20B
Exam 1 vA
University of California, San Diego
Department of Mathematics
Instructions
1. Write your Name, PID, and Section on the front of your Blue Book.
2. Write the Version of your exam on the front of your Blue Book.
3. No calculator