ANNUAL PLAN TEMPLATE
WHAT we will
do?
Direct Mail
Campaign
WHAT does it
look like?
We will design
and send out a
direct mail
campaign
highlighting a
story from one
of the children
that benefits
from our
organization.
To raise HOW
much money?
$20,000
WHO w
19. A group of statistics students decided to conduct a survey at their university to find the
average (mean) amount of time students spent studying per week. Assuming a standard
deviation of 6 hours, what is the required sample size if the error is to be
IHRN SCHOLARSHIP INFORMATION
Justice Sector Reform: Applying Human Rights Based Approaches
(OJIR17)
National University of Ireland, Maynooth, Ireland
Monday 26th June 2017 to Friday 30th June 2017
Scholarship Information
The International Human Rights Net
Jack Wu
204431429
Statistics 100B
Homework 5
1
1
var ( ^ )=var ( X )= 2 var ( X i)= 2 n var ( X ) =
n
n
n
1 a.
2
d ln f ( x ) x
d ln f ( x ) x
x e
(
)
f
x
=
ln f ( x ) =x ln ln x !
= 1
= 2
b.
x!
d
d 2
1
1
= =
n n
x
nE 2
[ ]
Yes , lim var ( ^ ) =0
c.
n
Jack Wu
204431429
Statistics 100B
Homework 2
1. Part A
1
E [ X ] = ( 2.6+2.8+ 3+3.2+3.4 ) =3
5
2
1
E [ X 2 ]E [ X ] = ( 2.62+ 2.82+ 32 +3.22+ 3.42 )3 2=.08
5
E [ X i ] = 3
[ ]
n
E [ X ] =E
Xi
i=1
n
n
=
1
n i=1
Xi
n
1
n i=1
var ( X )=var
The variance of
Jack Wu
204431429
Statistics 100B
Homework 1
1
1. a. Binomial (5, 3 )
b.
1 t
e
e
2
1
=
=Geometric( )
t
2
2e 1 1 e t
2
c.
Poisson (2)
t
1 0 2 0 3 0
1
'
2. a. [ X ] =M x ( 0 )= 6 e + 3 e + 2 e =2 3
1 0 4 0 9 0
'
b. var ( X )=M x ( 0 )= 6 e + 3 e + 2 e =6
3
Jack Wu
204431429
Statistics 100B
Homework 4
n
Xi
1 a.
X i ber ( p ) L= p
i=1
n
( 1 p )
Xi
i=1
= p x ( 1p )
nx
ln L=x ln p+ ( nx ) ln1 p
d ln L x nx
x nx
x
=
=0 =
x xp=npxp x=np ^p =
dp
p 1p
p 1p
n
2
b.
[
]
d ln L x
1x
x
1x
n
n
n
1 p
= 2
nE 2
= 2 E [
Jack Wu
204431429
Statistics 100B
Homework 3
2
5
1 a.
b.
4
c.
25
2
2 a. 0.0228 (from the standard normal table)
16
20
1
Z i then Z N ( 0, 42 ) P ( Z> 2 )=P X>
=P X > =0.3085
b. let Z=
2
16
i=1
(
) ( )
c. 0.975
2
16
d. S =
( Z iZ )
i=1
c=
e.
f.
2
15
15 S
STATS 100B
Introduction to Mathematical Statistics
WF, 3:30-4:45 PM, GEOLOGY 3656
Instructor: Jingyi Jessica Li
WWW: https:/ccle.ucla.edu/course/view/17S-STATS100B-1
Office Hours: W 9:00-11:00 AM at 8141 MS, and by appointment
Teaching Assistant: Jiaying
University of California Los Angeles (UCLA)
DEPARTMENT OF STATISTICS
COURSE SYLLABUS (TENTATIVE)
Course:
Lecture Meeting:
Quarter:
Professor:
Office:
E-mail:
Phone:
Office Hours:
Textbook:
STAT 100B: Mathematical Statistics
TR 03:00-4:50 PM. Room Boelter
University of California, Los Angeles
Department of Statistics
Statistics 100B
Instructor: Nicolas Christou
Hypothesis testing
Elements of a hypothesis test:
1.
2.
3.
4.
Null hypothesis, H0 (claim about , p,
Alternative hypothesis, Ha (>, <, =
6 ).
Test
STATS 100B Quiz 3
Aug. 2, 2017
1. Suppose x1 , x2 , ., xn is a a random sample from a Bernoulli(p)
a Show the MLE
P
P of p
xi
L(X|p) = p P
(1 p)n xi
P
log L(X|p) = x
p) xi log(1 p)
i log p + n log(1
P
P
1
1
xi p1 n 1p
+ xi 1p
p log L(X|p) =
P
xi
= n = X
STAT 100B Final Exam Check List:
Understand and know how to derive Expected values, mean, variance and m.g.f.s in the
distributions summary table.
State and proof of the KEY Theorem.
Understand m.g.f. properties and their proofs.
Understand Methods of tra
University of California, Los Angeles
Department of Statistics
Statistics 100B
Instructor: Nicolas Christou
The Central Limit Theorem
Suppose that a sample of size n is selected from a population that has mean and standard
deviation . Let X1 , X2 , , Xn b
Transformation of Random Variables:
Techniques for finding the distributions of functions of random variables:
1) Distribution Function Technique:
We first find the region in
2) Inverse Mapping Technique (Method of Transformation)
Suppose we know the dens
Matmamak $o5c$ (ETFH 10:9 8)
agmxxk4%mw&m%
3,
ROG/\AOM V Cxfim\.q .;
xx; I N
Wen/us fazmmho) S aim"? cfw_PCuafatut \3553
~ \~ 315. _ ,
eq/oemcr: cg QWAVMVMQAOVS Rm [2,) V "f 4/
w.o. A Amrnw , . n 1'. o m r '
L / d > m M j . a 83:8 Mm(05\na\ q\g\r\>
University of California, Los Angeles
Department of Statistics
Statistics 100B
Instructor: Nicolas Christou
Probability Distributions - Summary
Distribution
Binomial
Geometric
Negative Binomial
Hypergeometric
Poisson
Distribution
Uniform
Discrete Distribu
Stat 100B
Quiz #2
Due In-Class Tuesday, July 25, 2017
Q1)
Q2)
2
Q3)
Q4) An insurance company wants to audit health insurance claims in its very large database of
transactions. In a quick attempt to assess the level of overstatement of this database, the
i
Name:_
Stat 100B
SID:_
Quiz #1
Due in class Tuesday July 11, 2017
Q1) Find the distribution of the random variable X for each of the following
moment-generating functions:
2
7 10
a) () = ( + )
9
9
b) () = 10(
1)
Q2) Let X follow the Poisson probability d
Chapter 8
Estimation of Parameters
The Method of Moments
Notation:
Definition: The kth sample moment is given by:
Suppose we wish to estimate two parameters
moments:
can be expressed in terms of the first two
Then the method of moments estimates are:
Exam
University of California, Los Angeles
Department of Statistics
Statistics 1003 _
Distributions related to the normal distribution
Three important distributions:
0 Chisquare (X2) distribution.
0 t distribution.
0 F distribution.
Before we discuss the X2,t,
Transformation of Random Variables:
0) Linear Transformation Case:
Techniques for finding the distributions of functions of random variables:
1) Distribution Function Technique:
We first find the region in
2) Inverse Mapping Technique (Method of Transform
University of California, Los Angeles
Department of Statistics
Statistics 100B
Instructor: Nicolas Christou
Probability Distributions - Summary
Distribution
Binomial
Geometric
Negative Binomial
Hypergeometric
Poisson
Distribution
Uniform
Discrete Distribu
UCLA Department of Statistics
STATS 100B Homework 1
Instructor: Jingyi Jessica Li
Due date: Friday, Apr 14, 2017 at the beginning of discussion
Please staple your homework and write down your name, UID and discussion section number clearly.
Problem 1 (15
University of California, Los Angeles
Department of Statistics
Statistics 100B
Instructor: Nicolas Christou
Homework 8 - Solutions
EXERCISE 1
Answer the following questions:
a. The lifetime of certain batteries are supposed to have a variance of 150 hours