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Stats: Chapter 10
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Chance/Random Phenomenon
Has
unpredictable
behavior in the
short
run but has a
regular
and predictable pattern in the
long
run
Probability
Studies the likelihood of occurrence of random events in order to predict the behavior of
defined
systems.
Only describes what happens in the long run
Sample Space
S
The set of all possible outcomes in a random phenomenon
The set of all outcomes are caleld
events
1
event is the subset of the sample space
Probability Model
Description of a random phenomenon consisting of a
sample space S
and a way of assigning probabilities to
events
Probability Rules
A number between 0 - 1 is a probability number
All possible outcomes together must have a probability of one
If two events have no outcomes in common the probability that one or the other occurs is the sum of their individual probabilities
The probability that an event occurs is 1 minus the probability that the event does
not
occur
e.g. If event 1 occurs 50% of the time and a diff event occurs 25% of the time, then the chance of one or the other occuring is 75%
Probability numbers. What does 0, 0.5, and 1 mean?
0 = never occurs
1 = always occurs
0.5 occurs half the trials
0 < P(A) <= 1
A number between 0 - 1 is a probability number
P(S) = 1
The sample space S always equals 1
P(A or B) = P(A) + P(B)
If A and B are
disjoints
if they have no outcomes in common
The chance of one of them occuring is the sum of the two probabilities
P(A does not occur) = 1 - P(A)
The probability of an event that does not occur is 1 - the probability that the event does occur
Discrete Probability Model
A model with a
finite
sample (has limits)
The prob of any event is the
sum
of the probabilities of all the values that make up the event
This model assigns each of these values a probability between 0 and 1 such that the sum of all the probabilities is 1
Continuous Probability Model
Assigns the probabilities as areas under a density curve
The probability of any event is the area under the curve above the values that make up the event
Random Variable
A variable whose value is a numerical outcome of a random phenomenon
Probability Distribution
The random variable X tells us what the
possible
values of X are and
how
probabilities are assigned to those values
Author
muk.muk
ID
42312
Card Set
Stats: Chapter 10
Description
Chapter 10 definitions
Updated
2010-10-15T03:53:38Z
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