Mathematical Methods · continuous RVs · manipulative

The mean is where the density balances

E(X) = ∫ x p(x) dx is the fulcrum of the lamina. Skew the tail — the peak stays put relative to the mass, and μ slides into the tail.

p(x) mode μ = E(X)
E(X) = μ
—

Skew

0.45

Lognormal density on a locked axis. σ stretches the right tail; the gold fulcrum is μ.

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