STAT 251 Lecture Notes - Lecture 3: Set Theory, Fair Coin, Mutual Exclusivity
Chapter 3 – Probability
Learning Outcomes
Demonstrate an understanding of the basic concepts of
probability and random variables.
Recall rudimentary mathematical properties of probability.
Describe the sample space for certain situations involving
randomness.
Explain probability in terms of long-term relative frequencies
in repetitions of experiments.
Recall what are meant by the terms independent, mutually
exclusive (disjoint) and complementary events.
Apply the definition of independence to attempt to determine
whether an assumption of independence is justifiable in a
given situation.
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Chapter 3 Learning Outcomes
Find probabilities of single events, complementary events
and the unions and intersections of collections of events.
Use Venn diagrams where appropriate to solve probability
problems
Apply the definitions of independence and conditional
probability to solve probability problems
Calculate posterior probabilities through tree diagrams or
Bayes theorem.
Use the law of total probability where appropriate to solve
probability problems
Compute the reliability (that is, the probability that a system
works) in simple circuits of independent components
connected in series and/or parallel given the reliability of
each component.
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Introduction to Probability
Random experiments
In statistics, the notion of an experiment differs somewhat from
that of an experiment in the physical sciences.
In statistical experiments, probability determines outcomes.
Even though the experiment is repeated in exactly the same
way, an entirely different outcome may occur. Outcome cannot
be determined beforehand.
Sample Space (denoted with S )
Sample space is the set of all possible outcomes of a random
experiment.
Event
An event is a subset of the sample space.
Usually denoted with capital letters e.g. A, B, C.
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Document Summary
Demonstrate an understanding of the basic concepts of probability and random variables. Describe the sample space for certain situations involving randomness. Explain probability in terms of long-term relative frequencies in repetitions of experiments. Recall what are meant by the terms independent, mutually exclusive (disjoint) and complementary events. Apply the definition of independence to attempt to determine whether an assumption of independence is justifiable in a given situation. Find probabilities of single events, complementary events and the unions and intersections of collections of events. Use venn diagrams where appropriate to solve probability problems. Apply the definitions of independence and conditional probability to solve probability problems. Calculate posterior probabilities through tree diagrams or. Use the law of total probability where appropriate to solve probability problems. Compute the reliability (that is, the probability that a system works) in simple circuits of independent components connected in series and/or parallel given the reliability of each component.
