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66 Cards in this Set
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- Back
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Probability is defined as...
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The numeric value representing the change, likelihood or possibility that a particular even will occur.
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An event that is certain to happen has a probability of
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1
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An event that has NO certainty to happen has a probability of
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0
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The three types of priority are...
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A priori
Empirical Subjective |
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A Priori is defined as...
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Probability of an occurrence is based on prior knowledge of the process involved.
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When each outcome is equally likely, the probability is known as...
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A Priori
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The equation for 'A Priori' is
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# of ways the event can occur DIVIDED BY
Total # of possible outcomes |
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A example of A priori is...
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Choosing black or red from a deck of cards
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Empirical Probability is defined as...
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Probability that is based on observable data.
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Probability that is based on observable data is known as...
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Empirical Probability
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An example of Empirical Probability is...
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Surveys
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Each possible outcome of a variable is referred to as an
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event
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This is described by a single characteristic
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A simple event
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Each side of a dice is described as
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A simple event
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An event with two or more characteristics is defined as
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A Joint Event
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Getting two heads when you toss a coin is an example of a
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A Joint Event
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The complement of something is represented by
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An apostrophe (A' means complement of A)
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What are the complements of the following....
*Heads on a coin *Five dots on a die |
*Tails
*Not getting five dots on a die |
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The collection of all possible events is called the
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Sample Space
(Heads & Tails on a coin) (One, Two, Three, Four, Five & Six on a die) |
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Two things to help you visualize sample spaces are...
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Contingency tables and Venn Diagrams
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In a Venn Diagram, A U B means...
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the total area of A and B
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In a Venn Diagram, A n B means...
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the intersection of A and B
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A simple probability refers to the probability of occurrence of a
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Simple Event
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An event that consists of a set of Joint Probabilities is know as
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Marginal Probability
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When two events cannot occur at the same time it is called
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Mutually exclusive
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When there is a sex of events and one of the events must occur it is called
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Collectively exhaustive
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A coin toss is mutually exclusive because
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You cant have heads and tails at the same time.
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A coin toss is collectively exhaustive because
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If heads does not occur, tails must occur
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Male and Female, Heads and Tails are both what kinds of events
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Mutually exclusive and Collectively exhaustive
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When dealing with an OR problem with A and B as variables... the equation would look like..
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P(A)+P(B) - P(A&B)
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Explain the following statement...
P(A|B) = P(A and B) / P(B) |
The Probability of B given A is equal to the probability of A and B divided by the probability of A
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When dealing with an ALSO problem with A and B as variables... the equation would look like..
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P(A|B) = P(A and B) / P(B)
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A decision tree is an alternative to
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A Contingency table
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When the outcome of one event does not affect the probability of occurrence of another even, the events are said to be
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Independent
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When dealing with dependence, if A and B percentages are equal then the events are...
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Independent
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When dealing with the Multiplication rule, multiply...
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The first possibility times -1 the second. (this is due to the first probability being subtracted from the second portion of the equation)
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A mathematical expression that defines the distribution of values for a continuous probability
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Probability density function
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The three types of distribution are...
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Normal, Uniform and Exponential
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This distribution is symmetrical and bell shaped.
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Normal Distribution.
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Normal Distribution has this type of visual...
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Bell shaped and symmetrical
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Most values tend to cluster around the mean when dealing with this type of distribution
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Normal Distribution
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During normal distribution, the vales tend to cluster around the...
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Mean
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During normal distribution, the mean is equal to the
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Median
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The Median is equal to the Mean during this type of distribution
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Normal
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There is normally no large positive or negative values when dealing with this type of distribution
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Normal Distribution
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A distribution that is shaped like a box is known as...
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Uniform Distribution
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During uniform distribution, each value has an equal probability of occurrence anywhere in the range of
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The smallest and largest value.
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Uniform distribution is symmetrical which means
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The Mean and the median are equal
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The skewed distribution is known as...
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Exponential Distribution
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When dealing with exponential distribution, it skews to the ______ and the _____is larger than the ________
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Right, Mean is larger than the median
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The range of an exponential distribution is...
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Zero to positive infinity
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When dealing with exponential distribution, large values are...
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Unlikely!
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When dealing with normal distribution, the probability of a single value and not a range is
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ZERO
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During normal distribution, the interquartile range is equal to
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1.33 standard deviations
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'e' is equal to
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2.718
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'π" is equal to
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3.1415
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"μ" is equal to
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The Mean
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"σ" is equal to
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Standard deviation. the Stan
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How do you calculate "σ"
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(1) Find the mean
(2) Subtract the mean from each single number to get a list of deviations (3) Square all these deviations (4) Sum all these deviations (5) Divide by one less than the total # of #'s (6) SQUARE ROOT of this number |
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How do you calculate "μ"
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Calculated by adding up all the numbers and dividing by the # of #'s
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"Z" is equal to
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Any continuous variable where
-INF < X < INF |
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The transformation formula is...
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Z= X - µ DIVIDED BY σ
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Uniform Distribution, probability density function
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1 DIVIDED BY b - a
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Uniform Distribution, probability density function...A and B... which is the larger function
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A is the MIN
B is the MAX |
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Uniform Distribution, Mean of the distribution
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µ = a+b DIVIDED BY 2
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Uniform Distribution, standard deviation formula
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σ = SQUAREROOT (b-a)^2 DIVIDED BY 12
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