統計機率函數的問題

題目有誤: F(n)=exp(-u)*u^n/n! , n=0,1,2,...
設投進k球之機率為f(k),則
f(k)=(投出k球進k球)+(投出k+1球進k球)+...
=(投出 k+n球進k球,不進n球), n=0,1,2,...
=Σ[n=0~infty] [exp(-u)*u^(n+k)/(n+k)!]*C(n+k,k)*p^k*(1-p)^n
= exp(-u)(up)^k / k!*Σ[n=0~infty] a^n/n! (where a=u(1-p) )
= exp(-u) (up)^k /k! * exp[u(1-p)]
= exp(-up)* (up)^k / k!, k=0, 1,2,3,...