Let \(X\) be a random variable such that the probability function of a distribution is given by \(P(X=0)=\frac{1}{2}\), …

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 \(P(X)\) is positive and even) respectively are: