f(x) = λ e^(-λ*x) for x >= 0

Γ(a+b)/(Γ(a)Γ(b))x^(a-1)(1-x)^(b-1) for a > 0, b > 0 and 0 ≤ x ≤ 1 where the boundary values at x=0 or x=1 are defined as by continuity (as limits).

f(x) = 1/(s^a Γ(a)) x^(a-1) e^-(x/s) for x ≥ 0, a > 0 and s > 0.

Γ(x+n)/(Γ(n) x!) p^n (1-p)^x for x = 0, 1, 2, ., n > 0 and 0 < p ≤ 1. Here parameterized using mu, where p = n / (n+mu)

f(x) = 1/(√(2 π) σ) e^-((x - μ)^2/(2 σ^2)) where μ is the mean of the distribution and σ the standard deviation.

f(x) = λ^x exp(-λ)/x! for x = 0,1,2,... and the mean (E(X))and variance (Var(X)) is ??.

f(x) = Γ((n+1)/2) / (√(n π) Γ(n/2)) (1 + x^2/n)^-((n+1)/2) It has mean 0 (for n > 1) and variance n/(n-2) (for n > 2).

f(x) = Γ((n1 + n2)/2) / (Γ(n1/2) Γ(n2/2)) (n1/n2)^(n1/2) x^(n1/2 - 1) (1 + (n1/n2) x)^-(n1 + n2)/2 It has mean 0 (for n > 1) and variance n/(n-2) (for n > 2).

f(x) = 1 / (2^(n/2) Γ(n/2)) x^(n/2-1) e^(-x/2) for x > 0. The mean and variance are n and 2n.

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