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  2. Law of total expectation - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_expectation

    The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations [2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value ⁡ is defined, and is any random variable on the same probability space, then

  3. Conditional expectation - Wikipedia

    en.wikipedia.org/wiki/Conditional_expectation

    This is not a constructive definition; we are merely given the required property that a conditional expectation must satisfy. The definition of E ⁡ ( X ∣ H ) {\displaystyle \operatorname {E} (X\mid {\mathcal {H}})} may resemble that of E ⁡ ( X ∣ H ) {\displaystyle \operatorname {E} (X\mid H)} for an event H {\displaystyle H} but these ...

  4. Tower rule - Wikipedia

    en.wikipedia.org/wiki/Tower_rule

    The tower rule may refer to one of two rules in mathematics: Law of total expectation , in probability and stochastic theory a rule governing the degree of a field extension of a field extension in field theory

  5. Probability theory - Wikipedia

    en.wikipedia.org/wiki/Probability_theory

    Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms .

  6. Law of total probability - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_probability

    The term law of total probability is sometimes taken to mean the law of alternatives, which is a special case of the law of total probability applying to discrete random variables. [ citation needed ] One author uses the terminology of the "Rule of Average Conditional Probabilities", [ 4 ] while another refers to it as the "continuous law of ...

  7. Tower property - Wikipedia

    en.wikipedia.org/?title=Tower_property&redirect=no

    This page was last edited on 15 June 2010, at 18:39 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may ...

  8. Probability interpretations - Wikipedia

    en.wikipedia.org/wiki/Probability_interpretations

    The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance.Does probability measure the real, physical, tendency of something to occur, or is it a measure of how strongly one believes it will occur, or does it draw on both these elements?

  9. Martingale (probability theory) - Wikipedia

    en.wikipedia.org/wiki/Martingale_(probability...

    In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values.