Canons Of
the Church
The early Christian Authorities fall into these
categories:
>Early Church Fathers (Ignatius, Polycarp, Justin Martyr, Irenaeus,
Clement, Tertullian, Origen, Eusebius, Didymus the Blind)
>Early Heretics and their Followers (Marcion and
Endogenous Process
Magmatism
Magma from Greek word thick ointment.
Is a molten and semi-molten rock mixture found under the surface of the Earth.
This mixture is usually made up of four parts:
A hot liquid base, called the melt
Minerals crystallized
Lec 17
M TH 201: P R O B A B ILITY
A N D S TATIS TIC S
Sec 6.6
Determining the z and x Values
When an Area Under the Normal
Distribution Curve Is Known
Find a point z such that the area
under the standard normal curve to
the left of z is .9251.
Find th
Lec 4
M TH 201: P R O B A B ILITY
A N D S TATIS TIC S
TU ES D AY 25 JU N E 2015
Supplem entary Exercises
Book Prem S M ann
Largest variance? Sm allest?
Properties ofs
SD is 0 when?
Strongly influenced by outliers like
the mean
M easures for G rouped D a
MTH201: PROBABILITY AND
STATISTICS
Sameen Reza
COURSE CONTENT: OUTLINE AND
ASSESSMENTS
Division of Marks:
Class Tests
Assignments
(4)
MidTerm Test
(1)
Final Exam
(2)
10
30
(1)
40
_
Total
20
100
MEANING OF STATISTICS
A term used to display data
A term used
Lec 11-29 July 2015
M TH 201: P R O B A B ILITY
A N D S TATIS TIC S
So far, in our discussion about discrete random
variables, we have been introduced to:
The probability distribution, which tells us which
values a variable takes, and how often it takes
MTH201: PROBABILITY AND
STATISTICS
LEC 2
18 June 2015
STEP 2
EXPLORATORY DATA ANALYSIS
condense large data sets by using tables graphs
and summary measures
In particular, EDA consists of:
organizing and summarizing the raw data,
discovering important
Lec 15,16
M TH 201: P R O B A B ILITY
A N D S TATIS TIC S
Ch 6.Prem S M ann
Continuous Random Variable and the
Normal Distribution contd.
Exam ples ofContinuous R.
Variables
the life of a battery,
heights of people,
time taken to complete an
examinati
Lec 6-2 July 2015
M TH 201: P R O B A B ILITY
A N D S TATIS TIC S
M utually Exclusive Events
Events that cannot occur together are called
mutually exclusive events. Such events do not
have any common outcomes.
If two or more events are mutually exclusive,
Lec 3
M TH 201: P R O B A B ILITY
A N D S TATIS TIC S
TU ES D AY 23 JU N E 2015
D istributions and Relationships
Distributions: exploring data
obtained from one variable at a time.
Examining Relationshipsexploring
data obtained from two variables at
a t
Lec 7-7 July 2015
M TH 201: P R O B A B ILITY
A N D S TATIS TIC S
Conditional Probability
The probability that event B occurs
given that event A has occurred is
called a conditional probability. It
is denoted P (B |A), which is read
the probability of B
Lec 19-6 August 2015
M TH 201: P R O B A B ILITY
A N D S TATIS TIC S
Inference
7.4 Shape ofSam pling
D istribution
assumed normal if the shape of the
population distribution is normal
assumed normal is sample size >30
Appl
ications ofthe Sam pling
D ist
Lec 5-30 June 2015
M TH 201: P R O B A B ILITY
A N D S TATIS TIC S
Probability
Leads to Inference
SAMPLE POPULATION?
This uncertainty is where probability
comes into the picture. We use
probability to quantify how much we
expect random samples to vary.
Lec 18-5 August 2015
M TH 201: P R O B A B ILITY
A N D S TATIS TIC S
Inference
7.1 Sam pling D istributions
Total of N= 5 students in class with
scores:
A. 1. 70
B. 2. 78
C. 3. 80
D. 4. 80
E. 5. 95
Population mean =? 80.6
Population standard deviation
Lec 11-29 July 2015
M TH 201: P R O B A B ILITY
A N D S TATIS TIC S
So far, in our discussion about discrete random
variables, we have been introduced to:
The probability distribution, which tells us which
values a variable takes, and how often it takes
Lec 13-31st July 2015
M TH 201: P R O B A B ILITY
A N D S TATIS TIC S
Ch 6.Prem S M ann
Continuous Random Variable and the
Normal Distribution
A continuous random variable can
assume any value over an interval or
intervals. Because the number of
values
Lec 10-28 July 2015
M TH 201: P R O B A B ILITY
A N D S TATIS TIC S
D iscrete Random Variable
Ch 5. Prem S Mann
Random Variable A random
variable is a variable whose value is
determined by the outcome of a
random experiment.
Random Variable:Theoretical
Lec 7-14 July 2015
M TH 201: P R O B A B ILITY
A N D S TATIS TIC S
G eneralM ultiplication Rule
Independent Events
P(B|A) = P( B and A)/P(A)
Therefore:
P(B and A) = P(B|A) * P(A)
Independent events
(Definition)Two events A and B are
said to be indepen