Homework 1 Due Monday, April 6th 2009
1. Read through the review material handouts found on my class website,
http:/www.uweb.ucsb.edu/~nbennett/PSTAT120B/120b.htm 2. Read Ch. 1, Sec 6.1-6.4 3. Hand in the following problems: 1.11 page 12 2.16 pag
Homework 2 The updated version Due Monday, April 13th 2009 in class
1. Please ask questions if you do not understand something in lecture; I will do my best to answer your question. The goal of this class is for you to learn statistics, and asking q
PSTAT 120B - Probability & Statistics
Class # 01-1 - Introduction
Jarad Niemi
University of California, Santa Barbara
29 March 2010
Jarad Niemi (UCSB)
Introduction
29 March 2010
1 / 18
Introduction
Days Goals
Days Goals
You know who I am I know who you ar
PSTAT 120B - Probability & Statistics
Class # 04-1- Midterm Review I
Jarad Niemi
University of California, Santa Barbara
19 April 2010
Jarad Niemi (UCSB)
Midterm Review I
19 April 2010
1 / 26
Class overview
Announcements
Announcements
Homework
Homework 3
Test topics
Distributions of functions of random variables
Method of distribution functions Alternative method of distribution functions Method of transformations Method of moment generating functions
Important sampling distributions
Sums and averages of
PSTAT 120B - Probability & Statistics
Class # 05-1- Condence intervals
Jarad Niemi
University of California, Santa Barbara
26 April 2010
Jarad Niemi (UCSB)
Condence intervals
26 April 2010
1 / 18
Class overview
Announcements
Announcements
Homework
Homewor
Homework 8 - Pstat 120B Winter 2017
Problem 1
An experimenter has prepared a drug dosage level that she claims will induce sleep for 80% of people
suffering from insomnia. After examining the dosage, we feel that the claim regarding the effectiveness
are
Confidence Intervals
Definition
A confidence interval for a confidence level is an interval inside which
the true but unknown parameter is with probability 1 . There are 3
types of confidence intervals:
Lower Confidence Interval
A lower CI L , is an inter
Homework 9 Solution - Pstat 120B Winter 2017
Problem 1
Two sets of elementary school children were taught to read by using different methods, 50 by each method.
At the conclusion of the instructional period, a reading test yielded the results x1 = 74 and
Homework 6 Solution - Pstat 120B Winter 2017
Problem 1
Let X1 ,X2 ,.,Xn denote a random sample of size n from a normal distribution with mean and variance
2 .
a) If is unknown and 2 is known, find the MLE M LE for estimation of .
b) Find the CRLB for esti
Homework 7 - Pstat 120B Winter 2017
Problem 1
When it comes to advertising tweens are not ready for the hard-line messages that advertisers often use
to reach teenagers. The Geppeto Group study found that 78% of tweens understand and enjoy adds that
are s
Hypothesis Testing
A hypothesis test is a tool to test the validity of a scientific/statistical
hypothesis.
As before, imagine that we are studying a random variable following a
distribution of known form with some unknown parameter .
Furthermore, suppose
Confidence Intervals
Definition
A confidence interval for a confidence level is an interval inside which
the true but unknown parameter is with probability 1 . There are 3
types of confidence intervals:
Lower Confidence Interval
A lower CI L , is an inter
Introduction
Review of Pstat 120A
Pstat 120B - Fall 2016
Jacob Lundbeck Serup
Department of Statistics and Applied Probability, UCSB
September 26. 2016
Jacob Lundbeck Serup
Pstat 120B - Fall 2016
Introduction
Review of Pstat 120A
Practical Information
My
PSTAT 120B - Probability & Statistics
Class # 10-2- Other reivew
Jarad Niemi
University of California, Santa Barbara
4 June 2010
Jarad Niemi (UCSB)
Other reivew
4 June 2010
1 / 11
Class overview
Announcements
Announcements
Homework
Homework 7 returned now
PSTAT 120B - Probability & Statistics
Class # 10-1- Hypothesis testing review
Jarad Niemi
University of California, Santa Barbara
2 June 2010
Jarad Niemi (UCSB)
Hypothesis testing review
2 June 2010
1 / 20
Class overview
Announcements
Announcements
Homewo
Review of PSTAT 120A Spring 2009
Probability Measure (Probability Function) Given a sample space, S, a probability function, Pr[.], is a function satisfying the following three conditions: i) Non-negative: ii) Total probability of 1: iii) Countable
Useful Mathematical Tools Spring 2009
Summation Notation
Product Notation
Factorial Indicator Function Let be a space with elements . Let A be a subset of . Then the indicator function of A is given by
Properties of the indicator function
i) ii)
HW 1 Solutions
1.11 a. b. c.
c = c + c + + c = nc. cy ( x
i =1 i =1 n i i =1 n i
n
= c(y1 + + yn) = c yi
i =1
n
+ y i ) = x1 + y1 + x2 + y2 + + xn + yn = (x1 + x2 + + xn) + (y1 + y2 + + yn)
Using the above, the numerator of s2 is
n n
PSTAT 120B - Probability & Statistics
Class # 05-2- Small-sample condence intervals
Jarad Niemi
University of California, Santa Barbara
28 April 2010
Jarad Niemi (UCSB)
Small-sample condence intervals
28 April 2010
1 / 19
Class overview
Announcements
Anno
PSTAT 120B - Probability & Statistics
Class # 08-1- Hypothesis testing
Jarad Niemi
University of California, Santa Barbara
17 May 2010
Jarad Niemi (UCSB)
Hypothesis testing
17 May 2010
1 / 19
Class overview
Announcements
Announcements
Homework
Homework 6
PSTAT 120B - Probability & Statistics
Class # 08-2- Sample size and CIs
Jarad Niemi
University of California, Santa Barbara
19 May 2010
Jarad Niemi (UCSB)
Sample size and CIs
19 May 2010
1 / 14
Class overview
Announcements
Announcements
Homework
Homework
PSTAT 120B - Probability & Statistics
Class # 08-3- P-values
Jarad Niemi
University of California, Santa Barbara
21 May 2010
Jarad Niemi (UCSB)
P-values
21 May 2010
1 / 15
Class overview
Announcements
Announcements
Homework
Homework 6 due Monday, 24 May @
PSTAT 120B - Probability & Statistics
Class # 09-1- Small sample tests
Jarad Niemi
University of California, Santa Barbara
24 May 2010
Jarad Niemi (UCSB)
Small sample tests
24 May 2010
1 / 16
Class overview
Announcements
Announcements
Homework
Homework 6
PSTAT 120B - Probability & Statistics
Class # 09-2- Hypothesis tests for variances
Jarad Niemi
University of California, Santa Barbara
26 May 2010
Jarad Niemi (UCSB)
Hypothesis tests for variances
26 May 2010
1 / 16
Class overview
Announcements
Announceme
PSTAT 120B - Probability & Statistics
Class # 09-3- N-P Lemma and LRTs
Jarad Niemi
University of California, Santa Barbara
28 May 2010
Jarad Niemi (UCSB)
N-P Lemma and LRTs
28 May 2010
1 / 11
Class overview
Announcements
Announcements
Homework
Homework 7
Transformations of Random Variables
Order Statistics
Sampling Distributions Related to the Normal Distribution
n m transformation
What do we mean by a transformation of a random variable?
Suppose:
I Y1 , Y2 , ., Yn
are n random variables.
I
The joint dist