Drag the sliders and watch the distribution reshape in real time — build intuition for what each parameter does.
Each distribution is defined by a few parameters. The normal is set by its mean (μ, where it's centred) and standard deviation (σ, how wide it is). The binomial needs the number of trials (n) and success probability (p). The Poisson needs a single rate (λ). Student's t needs the degrees of freedom (df). Move a slider and the whole curve is recomputed instantly.
The total area under any probability curve is always exactly 1. When you increase the standard deviation the data spreads over a wider range, so the curve must get shorter to keep that area at 1. Higher σ = flatter and wider; lower σ = taller and narrower.
The t-distribution has heavier tails than the normal when the degrees of freedom are small — that's what makes small-sample tests appropriately cautious. As df grows, the tails thin out and t converges to the standard normal. Slide df up and watch the dashed normal curve and the t-curve merge. See degrees of freedom explained.
When n is large and p isn't too close to 0 or 1 — a common rule is np ≥ 5 and n(1−p) ≥ 5. Set p = 0.5 and raise n, and the binomial bars trace out a bell shape. Set p near 0 with large n and it instead looks like a Poisson distribution.