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Expected Value

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Agenda

  • What is Expected Value?
  • Practice

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What is Expected Value?

What do we expect will happen?

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What is Expected Value?

  • Consider a fair coin, tossed 10 times
  • We would expect to see 5 heads and 5 tails
  • But we know it is also possible to end up with 10 heads or 10 tails and any combination in between

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What is Expected Value?

  • Consider a fair coin, tossed 10 times
  • We would expect to see 5 heads and 5 tails
  • But we know it is also possible to end up with 10 heads or 10 tails and any combination in between
  • The expected value of a random variable X is the arithmetic mean of all independent realizations of X

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What is Expected Value?

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  • The definition seems strange but matches our intuition with calculations

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Example

  • Single coin toss and X is the number of heads
    • S={H,T}, X(H)=1, X(T)=0
    • P(X=0)=P(X=1)=½
    • E(X)=0(½)+1(½)=½
  • Note that E(X) is not among the values that are possible
    • This frequently happens!

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Expected Value

  • Expected value is often combined with:
    • Histograms/Binning
      • Use the central value of each bin
    • Weighted averages
    • Tables of discrete random variables

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Practice

We expect that understanding follows practice

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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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