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
Continuous Random Variables and Distributions
STAT 1210
Probability and Statistics
(STAT 1210)
First Semester 2011
1 / 32
Probability Density
Let X be the IQ score of people.
n
1
2
3
4
5
7
20
40
0.1
0
0.1
50
60
70
80
90
100
110
120
130
140
150
60
70
80
90
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
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 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 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 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 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 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 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 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 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
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
Bayes Theorem
STAT 1210
Probability and Statistics
(STAT 1210)
First Semester 2011
1 / 16
Sensitivity of a Test
A new method for testing swine u . . .
For all infected people, it guarantees 100% correct.
. . . Do you think that it is useful?
(STAT 1210)
F
Discrete Random Variables and Distributions
STAT 1210
Probability and Statistics
(STAT 1210)
First Semester 2011
1 / 45
Random Variable
Denition
A random variable is a variable that assumes numerical values
associated with the random outcomes of an experi
Descriptive Statistics
STAT 1210
Probability and Statistics
(STAT 1210)
First Semester 2011
1 / 44
Descriptive Statistics
Three major ways to summarize data:
Tabular presentation such as the frequency distribution, the
cumulative frequency distribution an
Comparing Two Populations
STAT 1210
Probability and Statistics
(STAT 1210)
First Semester 2011
1 / 54
Two Population Means
Consider the following example:
Example
Suppose we have two populations of individuals. One population
(population 1) has experience
Analysis of Variance
STAT 1210
Probability and Statistics
(STAT 1210)
First Semester 2011
1 / 16
Completely Randomized Design
A completely randomized design is a design for which treatments are
randomly assigned to the experimental units, or in which inde
Parameter Estimation
STAT 1210
Probability and Statistics
(STAT 1210)
First Semester 2011
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Statistical Inference
A parameter is a numerical descriptive measure of a population.
Because parameter is based on the observations in the population, its
va
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
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
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
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