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  2. Algebra of random variables - Wikipedia

    en.wikipedia.org/wiki/Algebra_of_random_variables

    List of convolutions of probability distributions – the probability measure of the sum of independent random variables is the convolution of their probability measures. Law of total expectation; Law of total variance; Law of total covariance; Law of total cumulance; Taylor expansions for the moments of functions of random variables; Delta method

  3. Inclusion–exclusion principle - Wikipedia

    en.wikipedia.org/wiki/Inclusion–exclusion...

    The double-counted elements are those in the intersection of the two sets and the count is corrected by subtracting the size of the intersection. The inclusion-exclusion principle, being a generalization of the two-set case, is perhaps more clearly seen in the case of three sets, which for the sets A , B and C is given by

  4. Combinatorial principles - Wikipedia

    en.wikipedia.org/wiki/Combinatorial_principles

    The rule of sum is an intuitive principle stating that if there are a possible outcomes for an event (or ways to do something) and b possible outcomes for another event (or ways to do another thing), and the two events cannot both occur (or the two things can't both be done), then there are a + b total possible outcomes for the events (or total possible ways to do one of the things).

  5. List of logarithmic identities - Wikipedia

    en.wikipedia.org/wiki/List_of_logarithmic_identities

    The following summation/subtraction rule is especially useful in probability theory when one is dealing with a sum of log-probabilities: ... Subtracting from each ...

  6. Complementary event - Wikipedia

    en.wikipedia.org/wiki/Complementary_event

    This result cannot be right because a probability cannot be more than 1. The technique is wrong because the eight events whose probabilities got added are not mutually exclusive. One may resolve this overlap by the principle of inclusion-exclusion , or, in this case, by simply finding the probability of the complementary event and subtracting ...

  7. Law of total variance - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_variance

    Then the first, "unexplained" term on the right-hand side of the above formula is the weighted average of the variances, hσ h 2 + (1 − h)σ t 2, and the second, "explained" term is the variance of the distribution that gives μ h with probability h and gives μ t with probability 1 − h.

  8. Probability - Wikipedia

    en.wikipedia.org/wiki/Probability

    Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to ...

  9. Law of the unconscious statistician - Wikipedia

    en.wikipedia.org/wiki/Law_of_the_unconscious...

    In probability theory and statistics, the law of the unconscious statistician, or LOTUS, is a theorem which expresses the expected value of a function g(X) of a random variable X in terms of g and the probability distribution of X. The form of the law depends on the type of random variable X in question.