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  2. Chain rule (probability) - Wikipedia

    en.wikipedia.org/wiki/Chain_rule_(probability)

    In probability theory, the chain rule [1] (also called the general product rule [2] [3]) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities.

  3. Probability - Wikipedia

    en.wikipedia.org/wiki/Probability

    These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency ...

  4. List of unsolved problems in statistics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    The notable unsolved problems in statistics are generally of a different flavor; according to John Tukey, [1] "difficulties in identifying problems have delayed statistics far more than difficulties in solving problems." A list of "one or two open problems" (in fact 22 of them) was given by David Cox. [2]

  5. Conditional probability - Wikipedia

    en.wikipedia.org/wiki/Conditional_probability

    The conditional probability can be found by the quotient of the probability of the joint intersection of events A and B, that is, (), the probability at which A and B occur together, and the probability of B: [2] [6] [7] = ().

  6. Buffon's needle problem - Wikipedia

    en.wikipedia.org/wiki/Buffon's_needle_problem

    Similar to the examples described above, we consider x, y, φ to be independent uniform random variables over the ranges 0 ≤ x ≤ a, 0 ≤ y ≤ b, − ⁠ π / 2 ⁠ ≤ φ ≤ ⁠ π / 2 ⁠. To solve such a problem, we first compute the probability that the needle crosses no lines, and then we take its complement.

  7. Independence (probability theory) - Wikipedia

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

    Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.

  8. NYT ‘Connections’ Hints and Answers Today, Sunday, December 15

    www.aol.com/nyt-connections-hints-answers-today...

    We mean it. Read no further until you really want some clues or you've completely given up and want the answers ASAP. Get ready for all of today's NYT 'Connections’ hints and answers for #553 on ...

  9. Notation in probability and statistics - Wikipedia

    en.wikipedia.org/wiki/Notation_in_probability...

    The probability is sometimes written to distinguish it from other functions and measure P to avoid having to define "P is a probability" and () is short for ({: ()}), where is the event space, is a random variable that is a function of (i.e., it depends upon ), and is some outcome of interest within the domain specified by (say, a particular ...

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