1. John Theberge (noted wolf researcher in Algonquin Park) catches and
collars 67 wolves. He assumes that he has captured a random sample of
animals. For each of the animals he determines whether or not they are
coyote cross-breeds. He notices that 17 are
Lecture 23
th March 2015
4
When do we add or subtract from the value of
X?
ALWAYS draw a picture
Pr(a<X<b)
If X is binomial then the continuity correction
for X should be
Exercise 12.9: Forty percent of
postmenopausal women have low bond
density (osteope
Lecture
October 31, 2011
Chapter 5
Sampling Distribution ofY (contd)
Mean and Standard Deviation of
the Sample Mean
Suppose a population has parameters
given by the mean and the standard
deviation
The sample meanY is the statistic used
to estimate . Th
Lecture 4
th Jan 2014
12
Outliers
These are values that are more extreme than the
others in the data.
For example: 1, 5, 7, 1000
Outlier?
For example: -0.6, -10, -2.5, 0, 1, 0.6
Outlier?
Buffer Solution
9.1
4.1
8.1 7.8 7.0 6.8 5.4 5.4 4.1 3.8
Nanoparticle
Lecture 5
th Jan 2015
14
Example 2.3.1: Weight Gain of Lambs: The
following data are the two-week weight gains (lb) of
six young lambs of the same breed that have been
raised on the same diet:
11, 13, 19, 2, 10, 1
Calculate the standard deviation.
Buffe
Lecture 6
th Jan 2015
16
The Histogram (Chapter 1, pg 14)
Is another graphical technique that can be used to
represent data.
Used to describe the data (i.e shape, spread, centre,
outliers, etc)
A Histogram is an example of a Frequency distribution.
We bui
Lecture 9
rd Jan 2015
23
Probability (Chapters 9 and
10)
Introduction to Probability:
We can define probability in 3 ways.
1.Subjective
2.Relative Frequency
3.Mathematical/ Classical
Subjective
Based on intuition, we guess what the probability
is.
Examp
Lecture 11
th Jan 2015
28
Dice example contd:
Suppose we roll a die once and let
A=cfw_Roll an even number and
B=cfw_The number is greater than 3
Find Pr(A|B)
Example: What is the probability that a
randomly selected person smokes, if
that person has Low
Lecture 10
th Jan 2015
26
Example: In a study of the relationship
between health risk and income, a large
group of people were asked a series of
questions. Some results are shown
below.
Low
Income
Medium
High
Total
Smoke
634
332
247
1213
Dont
smoke
Total
Lecture 7
th Jan 2015
19
Examining Relationships
Between Variables
Problem: Do people who attend a
diabetes control class manage their blood
glucose levels better than those that
received individual instruction?
What are a few things that we observe
whe
Lecture 17
th Feb 2015
11
Example:
Coliform bacteria occur in river water
with an average intensity of 1 bacteria
per 10 cubic centimeters (cc) of water.
Find:
a) The probability there are no bacteria in
a 20cc sample of water which is tested.
b) The p
Lecture 12
th Jan 2015
30
Question (ex 10.8): A study of the U.S.
clinical population found that 22.5% are
diagnosed with a mental disorder, 13.5%
are diagnosed with an alcohol related
disorder, and 5% are diagnosed with both
disorders.
a)What is the pro
Lecture 8
st Jan 2015
21
Example (e.x 3.7) The metabolic rate of a
person is the rate at which the body consumes
energy. Such a variable is important in studies of
weight gain, dieting and exercise. In this study
data on the lean body mass and resting
me
Lecture 15
th Feb 2015
6
Properties of Mean and Variance
We want to answer questions such as:
What happens to my mean and variance
when we add or subtract from our original
data values?
What happens to my mean and variance
when we multiply or divide the d
Lecture 13
nd Feb 2014
2
Determining Mean and Median
Median: value that the divides the area
under the curve in half.
Mean: is the balance point of the
curve.
Where:
For a symmetric density curve
Mean=median
For a Skewed curve:
Mean > Median if the curv
Lecture 16
th Feb 2015
9
Using Your Calculator
These are quite easy to calculate using
your calculator
Try looking for an nCr button on your
calculator
It can be a stand-alone button or you
may need to press the shift of 2nd
function button to access it
Lecture 14
th Feb 2015
4
F(x)
1
2
3
F(x)
1
2
3
F(x)
1
2
3
Example
The number of celery seeds that
germinate in a packet of 5 seeds has
the following cdf:
X
0
1
2
3
4
5
F(x)
0.1
0.2
0.3
0.5
0.8
1
Questions follow.
What is the probability that less than 2
494
Chapter 8 Sampling Distributions of Estimators
Exercises
1. Suppose that X1, . . . , Xn form a random sample from
the normal distribution with unknown mean and known
variance 2 . Let " stand for the c.d.f. of the standard
normal distribution, and let
Lecture 3
th Jan 2015
9
Describing Data (Chapter 2)
Types of Data
Quantitative (Numeric) Variable
Takes on a numeric value
Can be measured
Quantifies some aspect of an individual or thing.
Qualitative (Categorical) Variable
Takes on levels/ categories
484
Chapter 8 Sampling Distributions of Estimators
!
" #$1
m
c = 2(m+1)/2 (m)1/2 "
.
2
The marginal p.d.f. g(x) of X can be obtained from Eq. (8.4.8) by using the
relation
%
g(x) = f (x, w) dw
=c
%
0
w (m+1)/21 exp[wh(x)] dw,
where h(x) = [1 + x 2 /m]/2.
Probability and Statistics
Wenhao Gui
whgui@bjtu.edu.cn
Spring, 2016
P&S
Math@BJTU
Chapter 1: Introduction to Probability
Experiments and Events
Probability will be the way that we quantify how likely something
is to occur.
Definition: Experiment and Even
Probability and Statistics
Wenhao Gui
whgui@bjtu.edu.cn
Spring, 2016
P&S
Math@BJTU
Chapter 4: Expectation
4.1 The Expectation of a Random Variable
Summaries of the distribution, such as the average
value, or expected value, can be useful for giving people
Events
Founding Date of Rome: April 21, 8:05am, 753 BCE
Establishment of the Res Publica: By brutus when he took the throne over from tar
People:
Etruscans: urban, civilized, organized, they built massive cities, overlooking farmland and near
the water
Ae
CHAPTER 5
Events:
The Ides of March 44 BCE: the death of julius caesar. Brutus and cassius and the 60 leading
conspirator senators
Battle of Philippi 42 BCE: brutus and cassus and the last republican army was defeated by
Octavian and marc antony. The civi
Events:
AUC (753 BCE)- foundation of rome. Auc means ab urbe condita, years are named after consuls
or numbered from this date
People:
Maecenas: was the greatest patron/supporter of time. Virgil was patronized by Maecenas, who
was a friend of Augustus. Ho
STAT 202
Chapter (7)
Chapter 7
Samples and observational studies.
Chapter objectives
Observation versus experiment.
The role of randomness in sampling.
The simple random sample (SRS).
Other probability samples.
Sample surveys.
Cohorts and Case-Control Stu
Formula Sheet
Pn
1. x
=
2
i=1
2. s =
3. r =
xi
n
Pn
x)
i=1 (xi
n1
1
n1
2
=
Pn
x2i n
x2
n1
i=1
y
xi
x yi
i=1 ( sx )( sy )
Pn
S
4. r = xy
Sxx Syy
sum of squares of x
sum of squares of y
sum of cross products of x and y
13/01/2016
s
5. b = r sxy
6. a = y
STAT 202
Chapter (1)
Chapter 1
Picturing Distributions with Graphs
Chapter objectives
Know the definition of Statistics.
Understand the types of variables.
Ways to chart categorical data: bar graphs and pie charts.
Ways to chart quantitative data: his
STAT 202
Chapter 14 (a)
Chapter 14
Introduction to inference
Chapter objectives
Uncertainty and confidence.
Confidence intervals.
Confidence interval for a Normal population mean ( known).
Significance tests.
Null and alternative hypotheses.
The P-value.
STAT 202
Chapter (4)
Chapter 4
Regression
Chapter objectives
The least-squares regression line.
Finding the least-squares regression line.
The coefficient of determination, r 2
Outliers and influential observations.
Making predictions.
Association does no
STAT 202
Chapter (2)
Chapter 2
Describing Distributions with Numbers
Chapter objectives
Measure of center: mean and median.
Measure of spread: quartiles and standard deviation.
The five-number summary and boxplots.
IQR and outliers.
Identifying outli