Cumulative Function of Discrete Probability Distributions

Overview


When the set of outcomes is discrete (that is, countable and not continuous) the cumulative probability function can be dfined to be a sum a Heaviside Functions.

Example


Consider the following probability distribution.

  • {% Prob(X=1) = 0.25 %}
  • {% Prob(X=2) = 0.5 %}
  • {% Prob(X=4) = 0.25 %}

Then the cumulative function is given as
{% F(x) = 0.25 \times H(x-1) + 0.5 \times H(x-2) + 0.25 \times H(x-4) %}

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