x1 + ⋯ + xn n = 1 n n ∑ i=1 xi X a1 , … , aK n1 , … , nK n xi 1 n n ∑ i=1 xi = 1 n K ∑ k=1 nk ak = K ∑ k=1 nk n ak → K ∑ k=1 p(ak )ak , (n → ∞) 15 / 40
= ∫ 1 0 x a−1 (1 − x) b−1 dx B(a, b) = Γ(a)Γ(b)/Γ(a + b) x ∈ (0, 1) f(x) = x a−1 (1 − x) b−1 B(a, b) E[X] = a a + b , V [X] = ab (a + b)2(a + b + 1) 36 / 40