Title: Conditional Probability and Conditional Expectation
Abstract: This chapter reviews conditional probability and conditional expectation. In probability theory and statistics, given two jointly distributed random variables X and Y, the conditional probability distribution of Y given X is the probability distribution of Y, when X is known to be a particular value. It has been observed that calculations involving conditional probability mass function may lack a complete prescription to the same, thus, seemingly be a nuisance. The chapter presents an analysis of the dice game known as craps, which provides an educational example of the use of conditional probability in stochastic modeling. Here the win probability with fair dice is unfavorable, that is, it is less than half and with shaved dice, the win probability is favorable slightly better. What appears to be a slight change becomes, in fact, quite significant when a large number of games are played. To study a random sum: X = ξ1 + · · · + ξN when ξ1, ξ2,… are continuous random variables, we need to extend our knowledge of conditional distributions.
Publication Year: 1994
Publication Date: 1994-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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