random-variables #

Shows a random variable X as a mapping from outcomes ω in a sample space to numbers, then compares discrete vs continuous distributions. The bottom panels animate an interval (a,b] and demonstrate that P(a<X≤b)=F_X(b)-F_X(a): as a sum of PMF bars for a discrete RV and as an area under the PDF (integral) for a continuous RV, with the corresponding CDF step-curve vs smooth curve.

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Computing interval probabilities using the CDF difference F(b)-F(a)
02.Understanding why discrete distributions use a PMF (probability mass at points) while continuous distributions use a PDF (area over intervals)
03.Interpreting CDF plots as a complete distribution summary for modeling and simulation

technical notes #

Self-contained canvas draw function with retro grid-snapped rendering and green-on-black palette. Includes a small mouse interaction (mousemove) attached once to the canvas: x controls interval center, y controls interval width; otherwise it auto-animates. Uses simple normal PDF/CDF approximations (erf approximation) and a fixed discrete PMF to illustrate step vs smooth CDF behavior.

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