Normal distribution

Below you can find a plot of two density functions from a Normal distribution.

The one in blue is from a Normal(0,1) distribution and the other in red has the parameters defined in the sliders below. When you start the mean is set to 0 and the standard deviation is 1, so the two density function completely overlap.

Change those parameters using the sliders below and see how this affects the density function (area in red).

For more on the Normal distribution refer to:

• Normal Distribution – from Wolfram MathWorld
  
• Probability density function - Wikipedia

viewof mean = Inputs.range([-2, 2], {step: .1, label: "Mean", value:0})
viewof sd = Inputs.range([0.1, 5], {step: .1, label: "Standard deviation", value:1})

normal_densities = {
  // Create sequence from -6 to 6 with step 0.01
  const x = Array.from({length: 1201}, (_, i) => -6 + i * 0.01);
  
  // Standard normal density function
  function dnorm(x, mu = 0, sigma = 1) {
    return (1 / (sigma * Math.sqrt(2 * Math.PI))) * 
           Math.exp(-0.5 * Math.pow((x - mu) / sigma, 2));
  }
  
  // Calculate y values for both distributions
  return x.map(xi => ({
    x: xi,
    y: dnorm(xi), // standard normal
    y_for_parameters: dnorm(xi, mean, sd) // parameterized normal
  }));
}

Plot.plot({
  caption: `Normal density function`,
  x: {label: ""},
  y: {label:"Density"},
  marks: [
    Plot.ruleY([0]),
    Plot.areaY(normal_densities, {x: "x", y: "y", fill: "blue", fillOpacity:0.2}),
    Plot.areaY(normal_densities, {x: "x", y: "y_for_parameters", fill: "red", fillOpacity:0.2})
  ]
})