A random variable \(\xi\) takes on only integral nonnegative values with probabilities

(a) \(\mathrm{P}(\xi=k)=\frac{a^{k}}{(1+a)^{k+1}}, a>0\) is a constant (this is the Pascal distribution).

(b) \(p_{k}=\mathbf{P}\{\xi=k\}=\left(\frac{\alpha \lambda}{1+\alpha \lambda}\right)^{k} \frac{(1+\alpha) \ldots(1+(k-1) \alpha)}{k!} p_{0}\) for \(k>0\) where \(\alpha>0, \lambda>0\) and

\[ p_{0}=P\{\xi=0\}=(1+\alpha \lambda)^{-\frac{1}{\alpha}} \]

This is the Polya distribution.

Find \(\mathbf{M} \boldsymbol{\xi}\) and \(\mathbf{D} \xi\).