STAT400 / MATH 463, Spring 2016
Chapter 2, part II
Ruoqing Zhu, Ph.D. (rqzhu@illinois.edu)
https:/sites.google.com/site/teazrq/teaching/STAT400
February 12, 2016
1
The binomial distribution
The binomial distribution
Bernoulli distribution: mean and varia
STAT400 / MATH 463, Spring 2016
Chapter 3
Ruoqing Zhu, Ph.D. (rqzhu@illinois.edu)
https:/sites.google.com/site/teazrq/teaching/STAT400
February 26, 2016
1
Continuous random variables
Outline
The uniform distribution and its probably density function (pdf
STAT400 / MATH 463, Spring 2016
Chapter 7 Part I
Ruoqing Zhu, Ph.D. (rqzhu@illinois.edu)
https:/sites.google.com/site/teazrq/teaching/STAT400
April 10, 2016
1
Hypothesis testing
Outline
Hypothesis testing: type I and type II errors, p-value
Testing for
STAT400 / MATH 463, Spring 2016
Chapter 5
Ruoqing Zhu, Ph.D. (rqzhu@illinois.edu)
https:/sites.google.com/site/teazrq/teaching/STAT400
May 8, 2016
1
Several random variables
Outline
Independence of several random variables
Consequences on mean, variance
STAT400 / MATH 463, Spring 2016
Chapter 6 Part II
Ruoqing Zhu, Ph.D. (rqzhu@illinois.edu)
https:/sites.google.com/site/teazrq/teaching/STAT400
April 4, 2016
1
Confidence
mean
interval
for
one
Outline
Confidence interval (CI) for one mean
Known and unkno
STAT400 / MATH 463, Spring 2016
Chapter 2, part I
Ruoqing Zhu, Ph.D. (rqzhu@illinois.edu)
https:/sites.google.com/site/teazrq/teaching/STAT400
February 7, 2016
1
Discrete random variables
Discrete random variables
Concepts: Discrete random variables
Mul
STAT400 / MATH 463, Spring 2016
Chapter 6 Part I
Ruoqing Zhu, Ph.D. (rqzhu@illinois.edu)
https:/sites.google.com/site/teazrq/teaching/STAT400
March 13, 2016
1
Maximum likelihood estimator
Outline
Point estimator
Likelihood function and maximum likelihoo
STAT400 / MATH 463, Spring 2016
Chapter 4
Ruoqing Zhu, Ph.D. (rqzhu@illinois.edu)
https:/sites.google.com/site/teazrq/teaching/STAT400
March 6, 2016
1
Bivariate distributions
Outline
Joint pmf and pdf of two random variables
Marginal pmf and pdf
Indepe
STAT400 / MATH 463, Spring 2016
Chapter 6 Part III
Ruoqing Zhu, Ph.D. (rqzhu@illinois.edu)
https:/sites.google.com/site/teazrq/teaching/STAT400
April 8, 2016
1
Confidence interval for variances
Outline
Confidence interval (CI) for variances and standard
STAT400 / MATH 463, Spring 2016
Chapter 1, part I
Ruoqing Zhu, Ph.D. (rqzhu@illinois.edu)
https:/sites.google.com/site/teazrq/teaching/STAT400
January 22, 2016
1
Topics in STAT 400 / MATH 463
Chapters 1-5: Probability
Basic concepts and properties
Mean
STAT400 / MATH 463, Spring 2016
Chapter 1, part II
Ruoqing Zhu, Ph.D. (rqzhu@illinois.edu)
https:/sites.google.com/site/teazrq/teaching/STAT400
January 30, 2016
1
Bayes Theorem
Bayes Theorem
Concepts: Bayess theorem
How to update the probability (prior
STAT 1210 Probability and Statistics
Mid-term Examination
Answer all questions. Total marks: 100.
1. If X N (1, 14.44), nd (a) P (1 X < 4), (b) P (X > 0), (c) P (X = 2), (d)
P (X = 2) , (e) where P (X ) = 0.1071.
(20 marks)
2. If X follows the binomial di
Hypothesis Testing
STAT 1210
Probability and Statistics
(STAT 1210)
First Semester 2011
1 / 63
Hypothesis Testing
The purpose of hypothesis testing is to aid the researcher in reaching
a conclusion concerning a population by examining a sample from that
p
1. The American Red Cross says that about 45% of the U.S. population has Type O
blood, 40% Type A, 11% Type B, and the rest Type AB.
(a) Someone volunteers to give blood. What is the probability that this donor
i. has Type AB blood?
ii. has Type A or Type
In country X, two diseases (DA and DB) aect the development of children seriously when they are 10-year-old. It is known that the height of normal
5-year-old child is normally distributed with mean 90cm. The heights of 5year-old child having DA and DB are
STAT 1210 Probability and Statistics
Suggested Answers for Assignment 4
1. (a) df = n 1 = 11 1 = 10, t0.975 = 2.228, xA = 3.8182, sA = 4.9157.
4.9157
sA
= 3.8182 (2.228)
= 3.8182 3.3022
xA t1/2
n
11
= [0.5160, 7.1204]
(b) H0 : A 0, HA : A > 0
t0 =
xA 0
STAT 1210 Probability and Statistics
Assignment 4
Due date: 1 Dec 2011
Instructions:
a. Your answer for the hypothesis test should contain all of the following items: (i)
the hypotheses, (ii) the test statistic used and its value (or ANOVA table), (iii) t
STAT 1210 Probability and Statistics
Supplementary Exercise
Instructions:
a. Answer ALL the questions.
b. The full mark is 100.
c. Your answers for the hypothesis tests should contain all of the following items: (i)
the hypotheses, (ii) the test statistic
STAT 1210 Probability and Statistics
Assignment 3
Due date: 18 Nov 2011
Instructions:
a. Your answer for the hypothesis test should contain all of the following items: (i) the
hypotheses, (ii) the test statistic used and its value, (iii) the degree of fre
STAT 1210 Probability and Statistics
Assignment 2
Due date: 20 Oct 2011
1. A survey database shows that 25 percent of the adults in country X have been
tested for HIV at some point in their life.
(a) Suppose that an adult who has been tested for HIV at so
STAT 1210 Probability and Statistics
Suggested Answers of Assignment 1
1. (a) mean: 4, median: 3.5, mode: 1
(b) range: 12, IQR: 3 or 3.75, variance: 9.368, standard deviation 3.061
(c)
i. mean: 3.5, median, 3.5, mode: 1,3,4,5
ii. The possible outliers wer
STAT 1210 Probability and Statistics
Suggested Answers of Assignment 2
1. (a) The number of adults selected (X) is geometrically distributed (p = 0.25). Use
the formula
n
ar i = a + ar + ar 2 + + ar n =
g(a, r, n) =
i=0
a(1 r n+1 )
1r
i. P(X = 3) = (1 p)2
STAT 1210 Probability and Statistics
Assignment 1
Due date: 7 Oct 2011
1. The U.S. Energy Information Administration monitors all nuclear power plants operating in the United States. The following table lists the number of active nuclear
power plants oper
Simple Linear Regression
STAT 1210
Probability and Statistics
(STAT 1210)
First Semester 2011
1 / 49
Linkage between Two Variables
What does it mean when we say that
smoking causes lung cancer?
It is a statistical statement meaning that you are much more
Probability
STAT 1210
Probability and Statistics
(STAT 1210)
First Semester 2011
1 / 30
Experiment and Sample
An experiment is an act or process of observation that leads to a single
outcome that cannot be predicted with certainty.
A sample point is the m
Introduction
STAT 1210
Probability and Statistics
(STAT 1210)
First Semester 2011
1 / 17
Instructor:
Email:
Website:
Ofce:
Tel:
Dr. Liu, KI
kiliu@hkbu.edu.hk
http:/www.math.hkbu.edu.hk/kiliu
FSC 1207
3411 7024
Textbook:
Milton and Arnold, Introduction to