Chapter 12 Continuous Random Variables and their Probability Distributions

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Chapter 12Continuous Random Variables and
their Probability Distributions
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Probability Distributions of a Continuous Random
Variable

• For a continuous random variable X, a probability
  density function such that

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Probability Distributions of a Continuous Random
Variable

• For a continuous random variable X, a probability
  cumulative function

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Mean Standard Deviation of a Continuous Random
Variable
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Continuous Probability Distributions

• Continuous Uniform Distribution
• Normal Distribution
• Exponential Distribution
• Erlang and Gamma Distributions
• Weibull Distribution
• Lognormal Distribution
• Beta Distribution

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Continuous Uniform Distribution

• Probability Density Function
• Mean
• Variance

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Normal Distribution

• Probability Density Function, with parameter ?,
  where -?lt?lt?, and ?gt0
• Mean
• Variance

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Normal Distribution

• The curve is symmetric about the mean
• The mean, median, and mode are equal
• The tails of the curve extend indefinitely

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Standard Normal Distribution

• A normal random variable with parameter ?0, and
  ?1
• Cumulative Distribution
• Table II in Appendix A
• Convert x to z

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Standard Normal Distribution
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Exponential Distribution

• Probability Density Function, with mean ?, where
  ?gt0, and xgt0
• Cumulative probability
• Mean
• Variance

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Exponential Distribution
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Exponential DistributionAlternate Definition

• Probability Density Function, with rate ?, where
  ?gt0, and x?0
• Cumulative probability
• Mean
• Variance

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Exponential DistributionExample

• An HR department wishes to study the need for
  hiring new secretaries. It is estimated that the
  amount of time that a secretary stays in the job
  can be described as an exponential distribution
  with a mean of 26 months. The company just hired
  a new secretary. Calculate the probabilities of
  the following events
• The secretary has to be replaced within the first
  year.
• The secretary has to be replaced during the third
  year.
• The secretary remains in the position for more
  than 5 years