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  2. Probabilistic method - Wikipedia

    en.wikipedia.org/wiki/Probabilistic_method

    Thus, for sufficiently large n, property 2 holds with a probability of more than 1/2. For sufficiently large n, the probability that a graph from the distribution has both properties is positive, as the events for these properties cannot be disjoint (if they were, their probabilities would sum up to more than 1).

  3. Probability distribution - Wikipedia

    en.wikipedia.org/wiki/Probability_distribution

    In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment. [1] [2] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). [3]

  4. Law of total probability - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_probability

    [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 alternatives" in the continuous case. [5] This result is given by Grimmett and Welsh [6] as the partition theorem, a name that they also give to the related law of total expectation.

  5. Sum of normally distributed random variables - Wikipedia

    en.wikipedia.org/wiki/Sum_of_normally...

    This means that the sum of two independent normally distributed random variables is normal, with its mean being the sum of the two means, and its variance being the sum of the two variances (i.e., the square of the standard deviation is the sum of the squares of the standard deviations). [1]

  6. Borel–Cantelli lemma - Wikipedia

    en.wikipedia.org/wiki/Borel–Cantelli_lemma

    Borel–Cantelli lemma — If the sum of the probabilities of the events {E n} is finite = <, then the probability that infinitely many of them occur is 0, that is, = Here, "lim sup" denotes limit supremum of the sequence of events, and each event is a set of outcomes.

  7. Convolution of probability distributions - Wikipedia

    en.wikipedia.org/wiki/Convolution_of_probability...

    The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.

  8. Boole's inequality - Wikipedia

    en.wikipedia.org/wiki/Boole's_inequality

    In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. This inequality provides an upper bound on the probability of occurrence of at least one ...

  9. Bernoulli trial - Wikipedia

    en.wikipedia.org/wiki/Bernoulli_trial

    Graphs of probability P of not observing independent events each of probability p after n Bernoulli trials vs np for various p.Three examples are shown: Blue curve: Throwing a 6-sided die 6 times gives a 33.5% chance that 6 (or any other given number) never turns up; it can be observed that as n increases, the probability of a 1/n-chance event never appearing after n tries rapidly converges to 0.