Probability Definitions

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Probability Definitions

• Dr. Dan Gilbert
• Associate Professor
• Tennessee Wesleyan College

2
Definitions

• Probability
• The expected outcome of an activity
• A numerical statement about the likelihood that
  an event will occur
• Experiment
• An activity that produces an event
• Sample
• The set of all possible outcomes of an experiment

3
Definitions

• Classical probability
• The number of outcomes favorable to the
  occurrence of an event, divided by the number of
  possible outcomes
• Subjective probability
• Probability based on personal beliefs of the
  person making the probability estimate
• Event
• One or more of the possible outcomes of an
  experiment

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Definitions

• Mutually exclusive events
• Events which cannot happen together
• Non-mutually exclusive events
• Events which may or may not occur together

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Definitions
? not /

• Conditional probability
• The probability of one event occurring given that
  another event has occurred.
• Joint probability
• The probability of events occurring together or
  in succession
• Marginal probability
• The unconditional probability of one event
  occurring

6
Definitions

• Statistical independence
• The conditions in which the occurrence of one
  event has no effect upon the probability of any
  other event
• Statistical dependence
• The conditions in which the probability of some
  event is dependent upon or affected by the
  occurrence of some other event

P(A ??B) P(A) P(B)
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Definitions Chapter 5

• Random Variable
• A variable whose numerical value is determined by
  the outcome of a random experiment
• Discrete Random Variable
• A random variable whose value is obtained by some
  finite number
• Continuous Random Variable
• A random variable whose value is obtained from a
  continuous scale within a given interval, and has
  an infinite number of possible outcomes

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Discrete vs Continuous

• Discrete
• Counting

• Continuous
• Measuring

9
Definitions

• Probability Distribution
• A systematic listing of all the possible values a
  random variable can take on, plus their
  respective probabilities
• Discrete Probability Distribution
• A probability distribution in which the variable
  is allowed to take on only a limited number of
  values
• Expected value
• A measure of the central location of a random
  variable

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Definitions

• Binomial probability distribution
• A discrete probability distribution of the
  results of an experiment using the Bernoulli
  process
• Bernoulli process
• A process in which
• Each trial has only two possible outcomes
• The probability of the outcome of any trial
  remains fixed over time
• The trials are statistically independent

11
Definitions

• Poisson probability distribution
• A discrete distribution in which the probability
  of the occurrence of an event within a very small
  time period is very small, in which the
  probability of two or more events will occur
  within the same small time interval is
  effectively zero, and in which the probability of
  the occurrence of the event within one time
  period is independent of where that time period
  is.

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Chapter 6

• Continuous probability distribution
• A probability distribution in which the variable
  is presented to take on any variable within a
  given range
• Normal distribution
• A distribution in which the curve has a single
  peak, in which it is bell-shaped, in which the
  mean lies at the center of the distribution, and
  in which the two tails extend indefinitely and
  never touch