概率论公式

常用概率分布及其数学期望和方差 常用离散分布分布分布列pkp_{k}pk​或分布密度p(x)p(x)p(x)期望方差0−10-10−1分布pk=pk(1−p)1−k,k=0,1p_k=p^k(1-p)^{1-k},k=0,1pk​=pk(1−p)1−k,k=0,1pppp(1−p)p(1-p)p(1−p)二项分布b(n,p)b(n,p)b(n,p)pk=(nk)pk(1−p)n−k,k=0,1,⋯ ,np_k=\dbinom{n}{k}p^k(1-p)^{n-k},k=0,1,\cdots,npk​=(kn​)pk(1−p)n−k,k=0,1,⋯,nnpnpnpnp(1−p)np(1-p)np(1−p)泊松分布P(λ)P(\lambda)P(λ)pk=λkk!e−λ,k=0,1,⋯p_k=\frac{\lambda^k}{k!}e^{-\lambda},k=0,1,\cdotspk​=k!λk​e−λ,k=0,1,⋯λ\lambdaλλ\lambdaλ超几何分布h(n,N,M)h(n,N,M)h(n,N,M)pk=(Mk)(N−Mn−k)(Nn),k=0,1,⋯ ,r,r=min{M...

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