$\DeclareMathOperator{\p}{Pr}$ $\DeclareMathOperator{\P}{Pr}$ $\DeclareMathOperator{\c}{^C}$ $\DeclareMathOperator{\or}{ or}$ $\DeclareMathOperator{\and}{ and}$ $\DeclareMathOperator{\var}{Var}$ $\DeclareMathOperator{\E}{E}$ $\DeclareMathOperator{\std}{Std}$ $\DeclareMathOperator{\Ber}{Bern}$ $\DeclareMathOperator{\Bin}{Bin}$ $\DeclareMathOperator{\Poi}{Poi}$ $\DeclareMathOperator{\Uni}{Uni}$ $\DeclareMathOperator{\Exp}{Exp}$ $\DeclareMathOperator{\N}{N}$ $\DeclareMathOperator{\R}{\mathbb{R}}$ $\newcommand{\d}{\, d}$

The likelihood is the product of the heights of all the green connections from the sample points to the Gaussian curve.

To fit the candidate normal distribution to the sample:

  • Translate it by translating the top of the curve with your mouse.
  • Change its width (correlates with standard deviation) by translating either side of the curve with your mouse.
  • Fine-tune the position and width of the curve by clicking and holding your mouse button down as follows:
    • Above the top of the curve to make it taller (and therefore narrower),
    • In the area below the curve to make it shorter (and therefore wider), or
    • On either side of the curve to translate it.