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Lecture 5

MATH 141 Lecture 5: Statistics 9/20/2016
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Department
MATH - Mathematics
Course Code
MATH 141
Professor
Zhang

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Statistics
9/20/2016
Probability
The probability is a measurement of the chance
The probability is a number between 0 and 1, corresponding to 0% and 100%
Definitions
Experiment – A process (game) that lead to an outcome as observation that cannot be
predicted. (i.e. random outcome)
Sample Point – The most basic outcomes of an experiment. The sample points MUST be
mutually exclusive from each other.
Sample Space – The collection of all possible sample points.
Event – A specific collection of sample points which have a common property. An event
can be a subset of the sample space. The sample is also an event.
oImpossible event – The event that won’t happen ever. This will be an empty set
that contains no sample points.
oCertain Event – The event that will happen for sure. The sample space is a certain
event.
Notation
Events: Capital letters such as A, B, C…
oA = {Event description}
Probability: P
oP(A) = Probability / chance that A will happen
Impossible Event:  Phi (Fee)
Sample Space – S
P() = 0, and P(S) = 1
Properties of the Probability
The probability is a number measuring the chance. A number to be a probability needs
to satisfy the following:
oThe probability is a non-negative number and can be no larger than one, i.e. the
probability p satisfies 0<P<1
oThe total of probabilities of all sample points ins 1, i.e. the possibility of all
possible cases together. For example, in a sample space S, there are 5 sample
points; E1, E2, E3, E4, E5 thus P(E1) +P(E2) +P(E3) +P(E4) +P(E5) =1. Because the
total event of all possible sample points covers all possible results.
How to Compute Probability
Relative Frequency Approach
oRepeat the game as many times as you can, see how many times you win the
game (frequency fi winning the game). Divide by the total number of your trials.
oThe relative frequency approach is an approximation to the probability of
winning the game; when you enlarge the number if trials the approximation can
be improved.
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Description
Statistics 9/20/2016 Probability  The probability is a measurement of the chance  The probability is a number between 0 and 1, corresponding to 0% and 100% Definitions  Experiment – A process (game) that lead to an outcome as observation that cannot be predicted. (i.e. random outcome)  Sample Point – The most basic outcomes of an experiment. The sample points MUST be mutually exclusive from each other.  Sample Space – The collection of all possible sample points.  Event – A specific collection of sample points which have a common property. An event can be a subset of the sample space. The sample is also an event. o Impossible event – The event that won’t happen ever. This will be an empty set that contains no sample points. o Certain Event – The event that will happen for sure. The sample space is a certain event. Notation  Events: Capital letters such as A, B, C… o A = {Event description}  Probability: P o P(A) = Probability / chance that A will happen  Impossible Event:  Phi (Fee)  Sample Space – S  P() = 0, and P(S) = 1 Properties of the Probability  The probability is a number
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