Confidence Interval
(Section 8.5)
Lecture 15
March 8, 2016 (Tuesday)
1
Where Are We?
2
Basic concepts
1. Review: Point estimator
2. Interval estimator (or confidence interval): a rule specifying the method for using
the sample measurements to calculate tw

Sampling distributions related to
the normal distribution (section 7.2)
t-distribution and F-distribution
Lecture 11,
Feb 23, 2016 Tuesday
Review
Definition of degree freedom:
Let Y1, Y2, . . . , Yn be a random sample of size n from a normal distributio

The Central Limit Theorem (CLT, Section 7.3)
Lecture 12
Feb 25, 2016 (Thursday)
1
Review
T-distribution (when variance is unknown)
F-distribution (comparing two variances)
Y1, Y2, ., Yn are independent and follow the same normal distribution.
(1) What

Sampling distributions related to
the normal distribution (section 7.2)
Lecture 10,
Feb 18, 2016 (Thursday)
1
Why do we study the distributions for
functions of variables?
To do inference, for example,
Sample
estimate Population
Sample mean
estimate popu

Chapter 7: Sampling Distribution
and the Central Limit Theorem
Section 7.1 and 7.2: Sampling distribution related
to the Normal Distribution
Lecture 8
Feb 11, 2016 (Thursday)
Where Are We?
Review
Normal distribution
Standard Normal distribution
Theorem

Section 6.5 The method of
Moment-Generating Functions
Lecture 6-7
Feb 4 and Feb 9, 2016
1
Moment Generating Functions
To learn: Moments and Moment-Generating Functions
Section 3.9 (for discrete variables)
Section 4.9 (for continuous variables)
Review:

Section 6.6 Multivariate
Transformation Using Jacobians
Lecture 5
Feb 2, 2016 Tuesday
Review
Normal distribution and standard normal
distribution: pdf, mean, variance, symmetric,
empirical rule (Section 4.5, P178-184)
Joint pdf, marginal pdf, independen

MATH4305: Probability and Statistics
Lectures 1 -3
Jan 19, 21, and 26, 2016
1
Introduction
First 5 minutes: social time for you to get to know each other.
Please get the contact information (email and phone number) from 4-5 new
classmates in two weeks.

Section 6.4 method of
transformation (page 310-313)
Lecture 4
Jan 28, Thursday, 2016
1
Review
Method of distribution functions (or CDF
method)
Inverse function (e.g, y=f(x)=2x, what is the inverse function of
f? )
Increasing and decreasing functions
2

Parameter estimation
(section 8.1-8.3)
Lecture 13 -14
Mar 1 & 3, 2016 (Tuesday and Thursday)
1
Where are we?
2
Review
Y1, Y2, ., Yn follow the same normal distribution.
(1) What is the distribution of the sample mean?
(2) What is the distribution of the