Statistics simulators
Randomness, distributions and the patterns that emerge from them.
Central Limit Theorem
Add up n draws from any distribution, over and over. The sums and the means pile into a bell whatever the source looked like, and with ±1 coin steps each sum is a random walk spreading like √n.
Joint, Marginals & Conditionals
Every pair of values gets a square whose area is its probability. Drag a box over the table and read the joint, the marginals and a conditional off one selection.
Covariance Matrix
Every point and the mean are opposite corners of a rectangle, positive or negative by where the point sits. Covariance is the average of those signed areas, the variances are the squares, and correlation is what is left once the units are divided out.
Probability Density
Grains of sand fall where a random quantity lands and pile up; per unit of width the pile becomes the density curve. Then the area is the share of grains, a squeezed pile climbs past 1, and one exact point catches nothing.
Monte Carlo
Throw random darts at a box and count the hits: the fraction times the box is the area. Estimate π, the area under a curve or a ball's volume in ten dimensions, and watch the error fall like 1/√n.
Bayes' Theorem
See why a 90% accurate test for a rare disease is usually wrong when it says positive. 1,000 people as dots make the posterior obvious.
Maximum Likelihood
Slide a Gaussian over sample data and watch the likelihood rise and fall. The best fit lands on the sample mean and the spread that divides by n, not n − 1.
Wasserstein Distance
Measure the distance between two distributions as the least work to reshape one into the other, the area between their CDFs.
Information and Entropy
A bit is one yes/no answer. Find a card in 16 with four of them, see why rare news takes more questions, send the weather in 1.75 bits a day, and pour the questions flat to find the entropy.
KL Divergence
The extra surprise of believing Q while the world draws from P. Watch samples land and their surprise add up, see the gap as red and blue area, find why the two directions differ wildly, and fit a bell both ways.