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 :

[JEE Main 2021, 25 Jul (Shift 2)]

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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 :

[JEE Main 2021, 25 Jul (Shift 2)]

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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)=…

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