Lecture # 7- Beginning of Chapters 4
and 5
Basic Probability Concepts
• We now lay the foundation for the field of statistical inference by studying the
theory of probability
• Statistical Inference: A set of techniques that allows us to turn sample
evidence into conclusions about statistical populations of interest
• Theory of Probability: Calculus of the likelihood of specific occurrences
-Gives rise to entire field of inferential statistics
-Points to likely point us towards a likely truth even though we cant know the
truth with certainty.
(Beginning of Lecture #8)
• Experiment: Any repeatable process from which an outcome measurement,
or result is obtained (It is something we can repeat).
• Random Experiment
o Definition: An experiment whose outcome cannot be predicted with
certainty
o Any activity that results in one and only one of several clearly definied
possible outcomes (ie: a number), but that does not allow us to tell in
advance which of these will prevail in any particular instance
• Sample Space
o Definition: A listing of all the basic outcomes of a random experiment, also
known sometimes as the (Outcome Space, Probability Space)
o Examples: -Tossing a single coin one
-Rolling a single die once
-Drawing a single card once
• Random Event
o Definition: Subset of the sample space
• Simple Event
o Definition: An single basic outcome from a random experiment
o Univariable, Bivariate (2 variables), multivariate (more than 2 variables)
• Composite Event
o Any combination of two or more basic outcomes
Examples: Ask two people if interest rates are going up
They must awnser “yes” or “no”
Simple events: a =(Y, Y), a =(Y, N), a =(N, Y), a4=(N,N)
1 2 3 Sample Space: U= a1,a2,a3,a4
Could definie more interesting composite event such as event A
“at least on person said yes”, in which the event A1= [a1,a2,a3] while
A2=[a2]
How Random Events Relate
• Mutually Exclusive Events
o Definition: Random Events that have no outcomes in common
o Often also called disjoint or incompatible events
• Collectively Exhaustive Events
o Definition: Random Events that contain all basic outcomes in the sample
space
o When the appropriate random experiment is collected, one of these
events is bound to occur
Ie: ask 2 ppl if the interest is going up, if one person says yes than it is
successful (a1, a2, a3) and the other didn’t??
• Complementary Events
o Two random events for which all basic outcomes not contained in one
event are contained in the other event
o Such events are usually both mutually exhaustive at the same time
• Unisons of Events (logical operator U –symbol [or])
o All basic outcomes contained in one or the other event
• Intersections of Events (logical operator upsidedown U [and])
o All basic outcomes contained in one and the other event
*On the midterm he will give examples of outcomes and will ask if they are
mutually exclusive or collective exhaustive*
Probability Concepts
• Objective Probability:

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