Core stats Lecture1.1_August1
GBA462 Lecture 1.1 Events and Probability Chapters 3.1-3.4
COURSE INTRODUCTION A foundations course in statistical analysis and interpretation
Asking the right questions and identifying the appropriate methods
Probability,hypothesis testing,simple/multiple regression and higher order models
Will help in building your quantitative foundation Many examples and MS Excel will be used
All statistical computer packages require statistical understanding of assumptions and limitations
WHO AM I?
You can call me SERCAN(pronounced like surgeon with“a”instead of“e”)
Ph.D.candidate in Operations Management
MS from Simon School,BS(Industrial Engineering) from METU(Turkey)
Interested in teaching,having coffee at Tim Hortons, following politics and occasionally some research in big data
A FEW POINTS BEFORE WE START Academic integrity is very important
Let’s be friends but behave professionally
You may disturb yourself but not others!
Please have your name tags
PERFORMANCE EVALUATION
Assignments:4x7.5%=30%
Quizzes:4x7.5%=30%
Final Exam:40%
All quizzes and final exam are designed to be open note which means that you may use the lecture notes/book/ your in-class notes etc.and your laptop/calculator.On the other hand,all forms of communication including but not limited to internet,e-mails,chats,cellphone are strictly prohibited.
LASTLY...
Course schedule will be finalized within few days and posted on Blackboard
-This is due to Registrar’s Office mistake on class schedules
Office hours on Thursdays@12:30PM
My e-mail is sercan.sarigul@https://www.360docs.net/doc/577397230.html,
Any questions?
Statistics classifying, interpreting Statistical and
While purpose population
FUNDAMENTAL ELEMENTS
Data:-can be quantitative or qualitative
-former one refers to measurements that are
recorded on a numerical scale
-latter one refers to measurements that can only
be classified into categories
Population:the collection(set)of units we are interested in https://www.360docs.net/doc/577397230.html,ually,the information about all population is missing and indeed,not economical to gather.
Sample:a subset of data from a large set
Numerical measures of central tendency:mean,median and mode
Numerical measures of variation:variance and standard deviation
Numerical measure of relative standing:
-(p t?)Percentile is a number such that p%of the data falls below it and(100–p)%falls above it
-Quartiles are special cases:25t?percentile is lower quartile,50t?percentile is median and75t?percentile is upper quartile
Experiment: outcome
Sample experiment Sample
-Listing:
-Venn
SAMPLE SPACE EXAMPLES Experiment Sample Space
Toss a Coin, Note Face{Head, Tail} Toss 2 Coins, Note Faces{HH, HT, TH, TT} Select 1 Card, Note Color{Red, Black} Play a Football Game{Win, Lose, Tie} Inspect a Part, Note Quality{Defective, Good} Observe Gender{Male, Female}
EVENTS
Specific collection of sample points
Simple Event:contains only one sample point
Compound Event:describes the probabilistic outcomes from two or more events
For each example below name (i)simple and (ii)compound events -Weather temperature tomorrow.-The total unit sales of muffins in Buzz cafénext month.
-The outcomes of two coins we toss.
S: sals of hundreds of
units c: sales less than
100
TOSSING 2 COINS
Experiment:Toss 2Coins.Note Faces.
Sample Space S ={HH,HT,TH,TT}
S
HH TT TH
HT
Outcome Compound Event:At least one Tail
Mutually time,
Collectively Give
Numerical occur
P(Event), Probability The
Statistics population Probability
What’s single thing). So tail?
PROPERTIES OF PROBABILITY
A probability of0means that the respective event is impossible to happen:
-Is the probability of finding a suitcase with$1M0?
-How about the probability of rolling one die and getting7?
A probability of1means that the respective event will definitely happen no matter what:
-Is the probability of a tossed coin showing Head or Tail equal to1?
-How about the probability of raining at least once in the next3months in Rochester?
EQUALLY LIKELY PROBABILITY Each of T sample points is equally likely
P(sample point)=1/T
X=Number of outcomes in the event
T=Total number of sample points in Sample Space then P(Event)=X/T
STEPS FOR CALCULATING PROBABILITY Define the experiment;describe the process used to make an observation and the type of observation that will be recorded (roll a die)
Sum the sample points probabilities to get the event probability (1/6+…+…=)
List the sample points (1,2,3…….)and assign probabilities to them (equally …)
Determine the collection of sample points contained in the event of interest (even numbered faces=2,4,6)
UNIONS & INTERSECTIONS
Union:
-Outcomes occurring in either events A or B or both
-‘OR’statement
-∪symbol(i.e.,A∪B)
Intersection:
-Outcomes occurring in both events A and B at the same time
-‘AND’statement
-∩symbol(i.e.,A∩B)