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Question
Let X be a random variable such that the probability function of a distribution is given by $P(X = 0) = {1 \over 2},P(X = j) = {1 \over {{3^j}}}(j = 1,2,3,...,\infty )$. Then the mean of the distribution and P(X is positive and even) respectively are :
${3 \over 8}$ and ${1 \over 8}$
${3 \over 4}$ and ${1 \over 8}$
${3 \over 4}$ and ${1 \over 9}$
${3 \over 4}$ and ${1 \over 16}$

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