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A discrete random variable X has the law of distribution of Poisson with the parameter l > 0 if it takes on values 0, 1, 2, …, m, …(infinite countable set of values) with probabilities The series of distribution of the Poisson law has the following form: xi … m … pi e-l le-l l2e-l/2! … lme-l/m! … Since the sum of the series the basic property of distribution

A random variable X is continuous if its function of distribution is continuous at each point and differentiable everywhere but possibly finitely many points. The distribution function of a continuous random variable X which is differentiable everywhere but three points of break is shown at the picture. Theorem. The probability of a separately taken value of a continuous random variable X is equal to zero, i.e. P(X

Although M(X) yields the weighted average of the possible values of X, it does not tell us anything about the variation, or spread, of these values. For instance, although random variables W, Y, and Z, having probability mass functions determined by W = 0 with probability 1 All have the same expectation – namely, 0 – there is much greater spread in the possible value of Y than in those of W (which is a

It is frequently the case when an experiment is performed that we are mainly interested in some function of the outcome as opposed to the actual outcome itself. For instance, in tossing dice we are often interested in the sum of the two dice and are not really concerned about the separate values of each die. That is, we may be interested in knowing that the sum is 7 and not be concerned over whether the actual

If several trials are made and the probability of an event A for each trial doesn’t depend on outcomes of other trials, such trials are called independent from the event A. At various independent trials an event A can have either different probabilities or the same probability. We will further consider only such independent trials in which the event A has the same probability. We use below the notion of complex

Let an event A can happen only in case of appearance of one of incompatible events B1, B2, …, Bn forming a complete group. Since it isn’t known beforehand which of these events will happen, we call them by hypotheses. The probability of appearance of the event A is defined by the formula of total probability: (*) Assume that a trial has been made in result of which the event A was appeared. Pose the problem to

Let as a result of a trial n events independent in union or some of them (in particular, only one or none) can appear, so that the probabilities of appearance of each of the events are known. How can we find the probability that at least one of these events will happen? For example, if as a result of a trial three events can appear, then an appearance of at least one of these events means an appearance of either

Theorem. The probability of joint appearance of two events is equal to the product of the probability of one of them on the conditional probability of another event calculated in assumption that the first event has already happened: P(AB) = P(A) × PA(B) Remark. P(BA) = P(B) × PB(A). Since the event BA does not differ from the event AB, P(AB) = P(B) × PB(A). Consequently, P(A) × PA(B) = P(B)

Let events A and B be incompatible and let the probabilities of these events be known. How can we find the probability of A + B? Theorem. The probability of appearance of any of two incompatible events is equal to the sum of the probabilities of these events: P(A + B) = P(A) + P(B) Corollary. The probability of appearance of any of several pairwise incompatible events is equal to the sum of the probabilities of

Here is a typical problem of interest involving probability. A communication system is to consist of n seemingly identical antennas that are to be lined up in a linear order. The resulting system will then be able to receive all incoming signals – and will be called functional – as long as no two consecutive antennas are defective. If it turns out that exactly m of the n antennas are defective, what is the

Example. Let an urn contain 6 identical, carefully shuffled balls, and 2 of them are red, 3 – blue and 1 – white. Obviously, the possibility to take out at random from the urn a colour ball (i.e. red or blue) is more than the possibility to extract a white ball. Whether it is possible to describe this possibility by number? It appears it is possible. This number is said to be the probability of an event

17.1.В содержании протеста должны быть указаны причины, послужившие основанием к его подаче, а также подробно изложены обстоятельства, связанные с нарушениями положений настоящего Регламента и «Официальных Правил баскетбола

1.1.Соревнования проводятся в соответствии с «Официальными Правилами баскетбола ФИБА 2014» с учетом всех официальных изменений, уточнений, дополнений и интерпретаций отдельных статей «Официальных Правил баскетбола ФИБА 2014», а

РЕГЛАМЕНТОткрытого Чемпионата города Макеевки сезона 2016-2017г.г.СТАТЬЯ 1. ПРАВИЛА ПРОВЕДЕНИЯ СОРЕВНОВАНИЙ1.1.Соревнования проводятся в соответствии с «Официальными Правилами баскетбола ФИБА 2014» с учетом всех официальных

Регламент 15-го сезона Русскоязычной Лигой Профи Клубов (далее РЛПК).Регламент может быть дополнен в течение сезона и изменен при необходимости. Регламент вступает в силу с момента его опубликования, обо всех изменения, внесенных

12.1 Решением спорных вопросов в течение сезона занимается КРСМ. 12.1.1 КРСМ состоит из членов РЛПК. 12.1.2 В КРСМ может входить не более одного члена клуба. 12.1.3 Член клуба не может принимать решения, относящиеся к его клубу. 12.1.4 Состав

8.1 Команды, занявшие два последних места в ПД, выбывают в ВД, включая снявшиеся команды. Соответственно, команды ВД, занявшие первые места, переходят в ПД. 8.2 Команды ПД, занявшие 11-12 места, играют стыковые матчи (далее СМ) с

https://youtu.be/y3ZEh6Pd4oI Календарь4.1 Русскоязычная лига профи клубов проводится по принципу «каждый с каждым» в два круга, на своем поле или поле соперника, согласно жеребьевке. 4.2 Команды должны проводить матчи в соответствии с

Регламент 15-го сезона Русскоязычной Лиги Профи Клубов (далее РЛПК).Регламент может быть дополнен в течение сезона и изменен при необходимости. Регламент вступает в силу с момента его опубликования, обо всех изменения, внесенных