Probability Distributions Discrete Random Variables Outcomes and Events

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Probability Distributions- Discrete Random
VariablesOutcomes and Events
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Random Variables

• A random variable is a rule that assigns exactly
  one value to each point in a sample space for an
  experiment.
• A random variable can be classified as being
  either discrete or continuous depending on the
  numerical values it assumes.
• A discrete random variable may assume either a
  finite number of values or an infinite sequence
  of values.
• A continuous random variable may assume any
  numerical value in an interval or collection of
  intervals.

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Random Variables

• Question Random Variable x Type
• Family x Number of dependents in
  Discrete
• size family reported on tax
  return
•  
• Distance from x Distance in miles
  from Continuous
• home to store home to the store site
  
• Own dog x 1 if own no pet
  Discrete
• or cat 2 if own dog(s) only
  
• 3 if own cat(s) only
  
• 4 if own dog(s) and cat(s)

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Probability Distributions

• The probability distribution for a random
  variable describes how probabilities are
  distributed over the values of the random
  variable.

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Expectation

• The mean of the random variable X is called the
  expected value of X

its written E(X)
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Expectation - example
The expected value of X is -
E(X) 0 x 1/4 1 x 1/2 2 x 1/4
1
You would expect 1 head out of every 2
throws
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Activity

• Handout Page 414
• Exercise 15F
• 1-8