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Probabily and Statistics : Discrete Random Variable, Probability Mass Function and Cumulative Distribution Function

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A4. A4. Let X be a discrete random variable with range RX = {1, 2, ...}.
(a) Show that
(b) Suppose that X has probability mass function (pmf)
(i) Find the cumulative distribution function (cdf) of X.
(ii) Use (a) to find E(X).

IMPORTANT: Could you please add at the end of the question a list of formulae under relevant headings of other distributions I ask for. For example if I ask for binomial forumulae give all the formulae that would be required if the question was exactly the same except about the binomial distribution.
I only want the formulae, not the question re answered.

Additional distribution:
Continuous Random variables given instead (also formulae to find Cov(X, Y), exponential function.

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Solution Summary

Discrete random variable, probability mass functions and cumulative distribution functions are investigated The solution is detailed and well presented.