Statistics

Joint, Marginals & Conditionals

Every pair of values gets its own square of probability. Drag a box over the pairs you care about: the squares inside are the joint, each edge stacks up a marginal, and a marginal divided by its total is a conditional.

the x range, Athe y range, Bthe squares you enclosed

Drag a box across the table to choose an event

P(A and B)—

—

How the two are linked

Strength of the link 0.00

opposedtogether

Condition on

All the numbers

P(A), the columns—

P(B), the rows—

P(A and B)—

P(A) × P(B)—

P(B | A)—

everything adds to—

What to observe

With the link at independent, every box gives P(A and B) = P(A) × P(B). That equality is the definition of independence.
The bar under a selected column is that column stacked up: summing y out gives P(x), and its amber part is the slice your box kept.
The conditional on the right is the kept columns divided by P(A): the same shape, rescaled to add to 1, and its amber bars add to P(B | A).
Slide the link to together and a box on the diagonal holds more than the product predicts. Under opposed the product overestimates instead.

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