Probability Theory


Starting with axiomatic definition of probability and some simple propositions as immediate consequences, the concept of conditional probability and independence are introduced. Then random variables are defined and their expected values, variances, etc., are discussed, followed by the important concepts of independent random variables and conditioning when there is dependence. Finally, transforms of random variables and their distributions are examined.


σ-field; Random Variables; pdf and pmf; Independence; Expectation and Conditional Expectation.

1.1 Random Experiments and Their Outcomes

Probability theory is the systematic study of outcomes of a random experiment such as the roll of a die, or a bridge ...

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