Conditional Probability Mass Function

A Conditional Probability Mass Function is a Conditional Probability Function that is a Probability Mass Function.

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• Example(s):
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• Counter-Example(s):
  • Conditional Probability Density Function.
• See: Random Variable Vector, Bivariate Random Vector, Discrete Random Vector, Continuous Random Vector, Joint Probability Mass Function.

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References

2016

• (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Conditional_probability_distribution#Discrete_distributions Retrieved:2016-1-8.
  • For discrete random variables, the conditional probability mass function of Y given the occurrence of the value x of X can be written according to its definition as: : [math]\displaystyle{ p_Y(y\mid X = x)=P(Y = y \mid X = x) = \frac{P(X=x\ \cap Y=y)}{P(X=x)}. }[/math] Due to the occurrence of [math]\displaystyle{ P(X=x) }[/math] in a denominator, this is defined only for non-zero (hence strictly positive) [math]\displaystyle{ P(X=x). }[/math] The relation with the probability distribution of X given Y is: : [math]\displaystyle{ P(Y=y \mid X=x) P(X=x) = P(X=x\ \cap Y=y) = P(X=x \mid Y=y)P(Y=y). }[/math]

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