Outline
Definition of terms involving probability
Definition of probability
Set Theory
Mutual Exclusivity
Independence
IE 27 1st Sem AY 14-15
Session 2
Random Experiment
An experiment that can result in different
outcomes, even though it is repeated in t
EARTHQUAKE DRILL ON THURSDAY
Fourth Long Exam
6 December 2014 (Saturday)
1:00 4:00
Final Exam
13 December 2014 (Saturday)
8:00 12:00
Todays Agenda:
Hypothesis testing on two samples
Hypothesis
Testing
General Procedure for Hypothesis testing
Step
1:
Step
EARTHQUAKE DRILL ON THURSDAY
Fourth Long Exam
6 December 2014 (Saturday)
1:00 4:00
Final Exam
13 December 2014 (Saturday)
8:00 12:00
Todays Agenda:
Hypothesis Testing on Proportion
Choice of Sample Size
Hypothesis
Testing
General Procedure for Hypothesis
Name
H0
One-sample z-test
= 0
One-sample t-test
= 0
One-proportion z-test
p = p0
H1
0
> 0
< 0
0
> 0
< 0
p p0
p > p0
p < p0
Test Statistic
z0 =
x 0
/ n
t0 =
x 0
s/ n
x np0
np0 (1 p0 )
z0 =
2
2 0
2-test on 1 variance
Goodness of fit test
Paired t-t
Quiz 1 will be on Tuesday, September 1, 2014, coverage is
only up to this lecture
The Tentative Exam Schedule for IE 27 is as follows
September 16 (Tuesday) - First Long Exam
October 13 (Monday) - Second Long Exam
November 10 (Monday) - Third Long Exam
De
Todays Agenda:
More Conditional Probability
Multiplication Rule
Independence
Total Probability Rule
Bayes Theorem
Conditional Probability
Conditional Probability
Probability of occurrence of an event given
an occurrence of another known event
P(AB
P(A|B)
Please be prepared to have exercises every class
meeting
This means bringing your formula sheets,
statistics tables and calculators EVERY MEETING
Exercises every class meeting will be offsetting
quizzes for this part of IE 27
Todays Agenda:
Hypothesis Tes
First Quiz on Tuesday, YEHEY!
Bring your own calculators as sharing of calculators will
not be allowed
Answer sheets for the quiz will be provided
Todays Agenda:
Probability Distribution
Probability Mass Function
Cumulative Mass Function
Bernoulli Random
ANNOUNCEMENT
IE 27 THV (11:30-1:00)
WILL PERMANENTLY MEET AT
THE IE COMPLAB
IE 27 THW (1:00-2:30)
WILL MEET AT THE IE COMPLAB
ON TUESDAYS.
THURSDAY VENUES WILL EITHER
BE AT 415 OR IE COMPLAB
Todays Agenda:
Random Experiment,
Sample Space and Event
Introdu
IE 27: Probability & Statistics
Sample Problems: Set 1
1st Semester AY 2014-2015
Sample Problem 1. Given the following PMF answer the following questions
A. What value of k will make the PMF valid?
B. Construct the CDF of the given PMF
C. Find the mean an
IE 27: Probability & Statistics
Sample Problems: Set 1
1st Semester AY 2014-2015
Sample Problem 1. In a room of 10 people what is the probability that at least two people
share the same birthday?
Sample Problem 2. A newly installed machine correctly deter
Last time
Branches of Statistics
Descriptive and Inferential
Data Collection Methods
Sampling Techniques
Data Formats
Data Presentation
Statistical Measures
IE 27 1st Sem AY 14-15
Session 21
Statistical Measures
Measures of Central Tendency
Mean
Avera
Definitions
Statistics
The study of the collection, analysis,
interpretation, presentation and organization of
data.
Drawing conclusions from data
IE 27 1st Sem AY 14-15
Session 20
Definitions
Population
Set of all possible values of a particular
cha
Hypothesis Testing
We want to test whether a 1 liter bottle of coke
really contains 1 L. We obtained a sample of 10
bottles and took their volumes (in L), shown by the
following table:
1.003
1.01
1.003
1.002
0.994
0.981
0.981
0.98
1.008
0.985
Test the hyp
Last meeting
Counting Techniques
FPC
Combination
Permutation
Permutation with similar objects
IE 27 1st Sem AY 14-15
Session 6
Practice
How many ways can you line up 4 boys and 5
girls in a line if:
a.) there are no restrictions?
b.) boys and girls must
Announcements
Exam: Sept 16 (T), 5:30
Problem Set
To be released on Sept 3
Answered in yellow pad
Groups of 3 (choose your own)
Deadline: Sept 10, 5PM
IE 27 1st Sem AY 14-15
Session 5
Counting Techniques
In the past, we determined that the
probability
Announcements
Problem Set is out
Quiz on Wednesday, September 10
IE 27 1st Sem AY 14-15
Session 7
Last Meeting
Circular Permutations
Random Variables
PMFs
CDFs
Mean and Variance
IE 27 1st Sem AY 14-15
Session 7
Counting techniques and probability
Weve
Continuous Distributions
Consider the following function:
f(x) = 2x/25, for 0 x 5
0, otherwise
What is the probability that x = 5?
What is the probability that x is between 2 and 3?
What is the mean of the f(x)?
What is the variance of f(x)?
What is
Assessment
What have we learned?
Point estimates
Interval estimates
What do we still need to learn?
Hypothesis tests
IE 27 1st Sem AY 14-15
Session 25
Hypothesis Testing
In the 3rd LE coverage we learned about point
estimates, but we didnt really le
Last time
We discussed descriptive statistics
Data Collection Methods
Sampling Techniques
Data Formats
Data Presentation
Statistical Measures
Data Analysis Tools
Data Organization Tools
IE 27 1st Sem AY 14-15
Session 22
Review: Take Home Quiz
IE 27 1st S
Announcements
Long Exam on Monday
2.5 hours
Time?
IE 27 substitute teacher
Sir Gil Kenneth San Miguel
Nov 26 and 28
IE 27 1st Sem AY 14-15
Session 24
Last time
Constructing Confidence Intervals
CI for mean
CI for proportion
CI for variance/stand
Sampling Distribution
The probability distribution of a sample statistic
If a sample is taken from a population following a
normal distribution, then the sample also follows a
normal distribution
It is proven that the sample mean also follows a
normal
Lecture
Alternative form of H0
error
Probability of committing a type II error
Power of the test = 1 -
IE 27 1st Sem AY 14-15
Session 29
Review
7 Steps:
1.) State the Null Hypothesis, H0
2.) State the Alternative Hypothesis, H1
3.) Choose a level of
IE 27: Probability & Statistics
First Long Exam
1st Semester AY 2015-2016
8 September 2015
INSTRUCTIONS:
1. Use Black or Blue Ink Only.
2. No sharing of calculator.
3. No using of cell phones.
4. Properly label all pages with its corresponding problem num