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RV X with parameter λ > 0 that supports k = {0, 1, ...}

Review of Random Variables (RVs)

Cumulative Distribution Function

A RV X is defined by a function F_X(x), called a cumulative distribution function (CDF) of X, which has the following properties:

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Example

CDF of a RV:

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Probability

For a RV X and any value a, F_X(a) represents the probability that X is less than or equal to a, i.e.:

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Probability Space

F_X(x) defines a probability space, and

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Continuous RVs

If the CDF of F_X(x) of the RV X is a continuous function of x, then X is a continuous RV.

Example

CDF of a continuous RV:

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CDF of a non-continous RV:

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Probability Density Function