Abstract
Consider the random experiment consisting of tossing a coin. The only possible outcomes of the experiment are head (h) and tail (t). Repeating the experiment n = 50 times, assume we obtained the following sequence of results:
The outcome head occured n h = 21 times while tail occured n t = 29 times. The relative frequencies are respectively
In fact, we know that if the number n of repetitions of the experiment increases indefinitely, the relative frequencies tend towards fixed limits which, if the coin is fair, are both equal to 0.5. This is known as statistical regularity. The probability of an event E can be defined as the limit of the relative frequency r E = n E /n when the number of repetitions of the random experiment goes to infinity:
This is called Bernoulli’s law of large numbers.
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References
W. B. Davenport, Probability and Random Processes, McGraw Hill, 1970.
Y. K. Lin, Probabilistic Theory of Structural Dynamics, McGraw Hill, 1967.
A. Papoulis, Probability, Random Variables and Stochastic Processes, McGraw Hill, 1965.
E. Parzen, Stochastic Processes, Holden Day, 1962.
R. L. Stratonovich, Topics in the Theory of Random Noise, 1, Gordon and Breach, N-Y, 1963.
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© 1994 Springer Science+Business Media Dordrecht
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Preumont, A. (1994). Random Variables. In: Random Vibration and Spectral Analysis. Solid Mechanics and Its Applications, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2840-9_2
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DOI: https://doi.org/10.1007/978-94-017-2840-9_2
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