Class Conditional Probability Function

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A class conditional probability function is a conditional probability function that is a discrete probability function (for a discrete random variable).



  • (Wikipedia, 2011) ⇒
    • Consider the rolling of two fair six-sided dice.
      • Let [math]\displaystyle{ A }[/math] be the value rolled on die 1
      • Let [math]\displaystyle{ B }[/math] be the value rolled on die 2
      • Let [math]\displaystyle{ A_n }[/math] be the event that [math]\displaystyle{ A=n }[/math]
      • Let [math]\displaystyle{ \Sigma_m }[/math] be the event that [math]\displaystyle{ A+B \leq m }[/math]
    • … Suppose however we roll the dice many times, but ignore cases in which [math]\displaystyle{ A+B\gt 5 }[/math]. In what proportion of the remaining rolls would [math]\displaystyle{ A=2 }[/math]? … [math]\displaystyle{ A=2 }[/math] in 3 of these. The answer is therefore [math]\displaystyle{ \textstyle \frac{3}{10} = 0.3 }[/math]. We say, the probability that [math]\displaystyle{ A=2 }[/math] given that [math]\displaystyle{ A+B \leq 5 }[/math], is 0.3. This is a conditional probability, because it has a condition that limits the sample space. In more compact notation, [math]\displaystyle{ P(A_2 | \Sigma_5) = 0.3 }[/math].