Check sums and moments

The exponential series ∑λ^x/x!=exp(λ) makes the masses sum to 1 after multiplying by exp(-λ). Reindexing x p(x) gives E(X)=λ; reindexing x(x-1)p(x) gives E[X(X-1)]=λ². Thus E(X²)=λ²+λ and variance=λ. Bin(n,p) may be approximated by Poisson(np) when trials are independent, n is large and p small; this is not a rule based on n>20 alone.