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3.2.2 Binomial Distribution

Code

Vega-Lite Chart

{
  "$schema": "https://vega.github.io/schema/vega-lite/v5.json",
  "description": "Binomial Distribution PMF for different parameters",
  "data": {
    "sequence": {
      "start": 0,
      "stop": 20,
      "step": 1,
      "as": "k"
    }
  },
  "transform": [
    {
      "calculate": "pow(0.3, datum.k) * pow(0.7, 10-datum.k) * (factorial(10) / (factorial(datum.k) * factorial(10-datum.k)))",
      "as": "y1"
    },
    {
      "calculate": "pow(0.5, datum.k) * pow(0.5, 20-datum.k) * (factorial(20) / (factorial(datum.k) * factorial(20-datum.k)))",
      "as": "y2"
    },
    {
      "calculate": "pow(0.7, datum.k) * pow(0.3, 15-datum.k) * (factorial(15) / (factorial(datum.k) * factorial(15-datum.k)))",
      "as": "y3"
    }
  ],
  "hconcat": [
    {
      "width": 250,
      "height": 200,
      "title": "n=10, p=0.3",
      "mark": "bar",
      "encoding": {
        "x": {
          "field": "k",
          "type": "ordinal",
          "title": "Number of Successes"
        },
        "y": {
          "field": "y1",
          "type": "quantitative",
          "title": "Probability",
          "scale": {
            "domain": [
              0,
              0.3
            ]
          }
        },
        "color": {
          "value": "#004976"
        }
      }
    },
    {
      "width": 250,
      "height": 200,
      "title": "n=20, p=0.5",
      "mark": "bar",
      "encoding": {
        "x": {
          "field": "k",
          "type": "ordinal",
          "title": "Number of Successes"
        },
        "y": {
          "field": "y2",
          "type": "quantitative",
          "title": "Probability",
          "scale": {
            "domain": [
              0,
              0.2
            ]
          }
        },
        "color": {
          "value": "#7A0045"
        }
      }
    },
    {
      "width": 250,
      "height": 200,
      "title": "n=15, p=0.7",
      "mark": "bar",
      "encoding": {
        "x": {
          "field": "k",
          "type": "ordinal",
          "title": "Number of Successes"
        },
        "y": {
          "field": "y3",
          "type": "quantitative",
          "title": "Probability",
          "scale": {
            "domain": [
              0,
              0.25
            ]
          }
        },
        "color": {
          "value": "#486300"
        }
      }
    }
  ]
}