Lecture04 2010

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Unformatted text preview: Conditional Probability and Distribution Functions: Lecture IV Charles B. Moss August 27, 2010 I. Conditional Probability and Independence A. In order to define the concept of a conditional probability it is necessary to define joint and marginal probabilities. 1. The joint probability is the probability of a particular combination of two or more random variables. 2. Taking the role of two die as an example, the probability of rolling a 4 on one die and a 6 on the other die is 1/36. 3. There are 36 possible outcomes of the two die { 1, 1} , { 1, 2} , · · · { 2, 1} , { 2, 2} , · · · { 6, 6} . 4. Therefore the probability of a { 4, 6} given that the die are fair is 1/36. B. The marginal probability is the probability one of the random variables irrespective of the outcome of the other variable. 1. Going back to the die example, there are six different rolls of the die where the value of the first die is 4 { 4, 1} , { 4, 2} , { 4, 3} , { 4, 4} , { 4, 5} , { 4, 6} (1) 2. Hence, again assume that the die are fair the marginal probability of x1 = 4 is 1 AEB 6182 Agricultural Risk Analysis and Decision Making...
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This note was uploaded on 02/01/2012 for the course AEB 6182 taught by Professor Weldon during the Fall '08 term at University of Florida.

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