{
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  "lines" : [
    {
      "id" : "D851FD0B-21D2-5E1B-8B89-435E6FE7A302",
      "source" : "# An exact binomial probability"
    },
    {
      "id" : "069E6D24-33D6-5338-831E-3E2B870E3AFC",
      "source" : "\/\/ 8 fair coin flips, exactly 5 heads. ways is 8 choose 5."
    },
    {
      "id" : "B21E8E1E-5865-5C21-82D0-969B51B43877",
      "source" : "flips = 8"
    },
    {
      "id" : "DEB84D4C-6E05-5103-B987-AAC85C7247DB",
      "source" : "heads = 5"
    },
    {
      "id" : "DF50D5B9-8A9A-582E-A881-92FB75482802",
      "source" : "ways = fact(flips)\/(fact(heads)*fact(flips - heads))"
    },
    {
      "id" : "EFDFBFDE-F6A2-5AF5-A84E-E59F1F4EDE67",
      "source" : "one way = 1\/2^flips in %"
    },
    {
      "id" : "997D76CE-1D0A-5AE1-84D1-C30EF2013B7D",
      "source" : "probability = ways*one way in %"
    },
    {
      "id" : "6C557327-438D-54F1-BB9C-24DC7F79BDD4",
      "source" : ""
    },
    {
      "id" : "1991110E-06EB-5651-AD4C-A6E359891ED7",
      "source" : "# The normal curve"
    },
    {
      "id" : "DD076421-4413-5DBB-A8A1-C46D1AD5A725",
      "source" : "\/\/ Example: heights with mean 170 cm and standard deviation 10 cm."
    },
    {
      "id" : "20A2F2DC-364B-57CB-B89E-3C4F590D6034",
      "source" : "μ = 170"
    },
    {
      "id" : "B94A6370-F401-5160-ACD9-4107C888BB09",
      "source" : "σ = 10"
    },
    {
      "id" : "7E9C6BA4-AD29-5F9F-B3D6-4865755F2446",
      "source" : "density(x) = e^(-(x - μ)²\/(2*σ²))\/(σ*sqrt(2*π))"
    },
    {
      "id" : "234E1033-F011-5586-A3BB-183666199050",
      "source" : "plot(density(x), x, 130, 210)"
    },
    {
      "id" : "D783F891-2F12-5ECE-BF0F-0C77C78EA098",
      "source" : "within one σ = integral(density(x), x, μ - σ, μ + σ) in %"
    },
    {
      "id" : "C491D8ED-9B91-5485-8951-11A1B43D9F78",
      "source" : "within two σ = integral(density(x), x, μ - 2*σ, μ + 2*σ) in %"
    },
    {
      "id" : "6AED9E67-3DF5-520D-A492-C777046CB0A2",
      "source" : ""
    },
    {
      "id" : "D2A6B74C-2C32-593D-B07E-D666EDA8A572",
      "source" : "# Expected value"
    },
    {
      "id" : "F2614D9A-DE8E-5E13-AF83-0D15D8EE6BFF",
      "source" : "\/\/ A $500 prize with a 1 in 1,000 chance of winning."
    },
    {
      "id" : "E3B6280D-005A-5EDF-853B-E0AAC144A5C5",
      "source" : "prize = $500"
    },
    {
      "id" : "1B30019E-9764-5F6A-84A7-B90BA9544C7E",
      "source" : "chance = 1\/1000"
    },
    {
      "id" : "DDB6AD0E-1D52-54AC-A5AE-23044F7EEAB2",
      "source" : "fair price = prize*chance"
    }
  ],
  "numberStyle" : {
    "decimal" : ".",
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    "secondaryGroupSize" : 3
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  "title" : "Probability distributions"
}