Scientific papers, vol.4 by Rayleigh.

By Rayleigh.

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35) This quantity is often called the return period of the stochastic process.

Based on the conditional probability, it is possible to introduce the concept of statistical independence: event A is said to be statistically independent from event B if P(A I B) = P ( A ) , In other words, knowing that B has occurred does not change the probability of A. 13), it follows that if A and B are statistically independent P ( A nB) = P(A)P(B). 2) which is actually a logical dependence: knowing that A has occurred (X,= 1), guarantees that B cannot occur (X,= 0). 2 [l] There are two streams flowing past an industrial plant.

4 Probability laws As previously mentioned, to the generic random event E is associated an indicator variable X,which takes the value of 1 when the event occurs in the experiment and 0 when it does not. Correspondingly, a real number p(E) is assigned to measure the probability of E and which satisfies the three Kolmogorov axioms. 1 Union of non-mutually exclusive events Consider n events En not mutually exclusive. 2) for the union of the two events A and B. 9) the (linear) expectation operator.

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