def. Conditional Distribution. let be jointly distributed. Then the conditional probability distribution of given a specific value of is the conditional probability distribution.

  1. are discrete:
  1. are continuous:

  • if :


…the red line height divided by the orange line is the p.d.f conditional distribution . …the orange line is the value of the marginal distribution at .

thm. Continuous Multiplication Rule. let be jointly distributed. Then:

thm. Rule of Average Conditional Probability. let , Then: