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Probability Functions

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Agenda

  • Discrete Random Variables
  • Practice

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1.

Discrete Random Variables

What’s this mean?

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Discrete Random Variables

  • Consider rolling two tetrahedral dice
    • Faces are 1, 2, 3, 4
  • Describe the sample space

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Discrete Random Variables

  • Consider rolling two tetrahedral dice
    • Faces are 1, 2, 3, 4
  • Describe the sample space
    • S={11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44}
  • What are the possible totals of the faces?

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Discrete Random Variables

  • Consider rolling two tetrahedral dice
    • Faces are 1, 2, 3, 4
  • Describe the sample space
    • S={11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44}
  • What are the possible totals of the faces?
    • T={2, 3, 4, 5, 6, 7, 8}
  • T is called a Discrete Random Variable

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Discrete Random Variables

  • T is called a Discrete Random Variable
  • Discrete
    • Only contain certain values
  • Random
    • You won’t know the total in advance
    • Only after the dice are rolled
  • Variable
    • Can have 1 or more values

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Discrete Random Variables

  • Probability of the DRV

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  • Probability function assigns a probability to each possible value of the DRV
  • Properties
    • All prob are positive and <= 1
    • Sum of prob is 1

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Uniform Random Variable

  • A uniform random variable has all probabilities equal for all values
  • If there are n possible values then each probability is 1/n

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Uniform Random Variable

  • Let X represent the face value rolled on a regular 6-sided die.
  • Describe the probability of each outcome.

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Uniform Random Variable

  • Let X represent the face value rolled on a regular 6-sided die.
  • Describe the probability of each outcome:

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Uniform Random Variable

  • Let X represent the face value rolled on a regular 6-sided die.
  • Find the probability function of X

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Uniform Random Variable

  • Let X represent the face value rolled on a regular 6-sided die.
  • Find the probability function of X

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2.

Practice

What’s the probability of getting some practice in?

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Practice

  • Go to the Canva

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Credits

Special thanks to all the people who made and released these awesome resources for free:

  • Presentation template by SlidesCarnival

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