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- independence related to random variables. - suitable events involving the possible values of various random variables Independence of a Random Variable from an Event 'The occurrence of the conditioning event provides no new information on the value of the random variable.' The random variable \(X\) is independent of the event \(A\) if $$P(X = x and A) = P(X = x)P(A) = p_X(x)P(A), \quad \text{f..

Conditional PMFs, given the value of another random variable Properties of conditional PMFs. Contents Conditioning (1) - conditioning a random variable on an event - conditioning one random variable on another - summary of facts about conditional PMFs Conditioning (2) - conditional expectation - total expectation theorem + mean and variance of the geometric (example 2.17.) + The Two-Envelopes Pa..

Given a random variable X, one may generate other random variables by applying various transformations on X. If Y = g(X) is a function of a random variable X, then Y is also a random variable, since it provides a numerical value for each possible outcome. This is because every outcome in the sample space defines a numerical value x for X and hence also the numerical value y = g(x) for Y. If X is..

Connectivity with previous chapters To simply take the concepts from Chapter 1 (probabilities, conditioning, independence, etc.) and apply them to random variables rather than events, together with some convenient new notation. numerical values를 가지고 있으면 often useful to assign probabilities to them. Lecture note 기준 Random variables An assignment of a value (number) to every possible outcome Mathe..

Contents 2.1. Basic Concepts 2.2. Probability Mass Functions 2.3. Functions of Random Variables 2.4. Expectation, Mean, and Variance 2.5. Joint PMFs of Multiple Random Variables 2.6. Conditioning 2.7. Independence 2.8. Summary and Discussion Problems 위 개념들을 다음 글들에서 다루도록 하겠습니다 References Bertsekas, D. P., Tsitsiklis, J. N. (2008). Introduction to Probability Second Edition. Athena Scientific.