# Thread: Calculating E(X) and V (X)

1. ## Calculating E(X) and V (X)

Let X be a random variable taking values in the positive integers, with probability mass function of the form:

pX (k) = 2/3^(−k)

Does E(X) and V (X) exist for this pmf? and how should I calculate them? or why they are not exist?

Let X be a random variable taking values in the positive integers, with probability mass function of the form:

pX (k) = 2/3^(−k)

Does E(X) and V (X) exist for this pmf? and how should I calculate them? or why they are not exist?
Does $E(X) = \sum_{k = 1}^{+\infty} \frac{2k}{3^k}$ converge?

Does $E(X^2) = \sum_{k = 1}^{+\infty} \frac{2k^2}{3^k}$ converge?

### calculating V(x)

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