expected-value #

Shows expected value as a probability-weighted average (highlighting one term x·P(x) at a time) and as the long-run average: a running sample mean from repeated draws converges toward the theoretical E[X]. A bottom panel animates linearity by varying constants a and b and displaying E[aX+b] = aE[X]+b.

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Evaluating games of chance and making fair-bet decisions
02.Estimating average outcomes in A/B tests or simulations (Monte Carlo)
03.Computing expected cost/latency in systems with probabilistic behavior

technical notes #

Deterministic per-cycle sampling uses a simple xorshift32 PRNG so the animation is stable. The right panel plots the running mean approaching a fixed E[X] line; the left panel cycles a highlighted x·P(x) term. Layout scales with canvas size using scale=Math.min(w,h)/240 and snap-to-grid rounding for a blocky aesthetic.

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