Let $x$ be a random variable such that the probability function of a distribution is given by $P(X=0)=\frac{1}{2}, P(X=j) =\frac{1}{3^j}(j=1,2,3, \ldots, \infty)$. Then the mean of the distribution and $\mathrm{P}(\mathrm{X}$ is positive and even) respectively are:
