i). suppose x has a binomial distribution with probability of success p over n trials. Show that E[1/(1+x)]=[1-(1-p)n+1]/[p(n+1)].

ii). suppose now x has a negative binomial distribution with density

P(X=k)=k-1Cn-1 pnqk-n with q=1-p and K>=n, prove that for any function f(x),

E[qf(x)]=E[(x-n)f(x-1)/(x-1)]