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Article title THE ANALYSIS OF THE FUNCTIONS USED FOR DEFINITION OF PROBABILITIES OF RANDOM VARIABLES WITH THE NORMAL LAW OF DISTRIBUTION
Authors Yu.M. Tulyakov, P.A. Ruzanov
Section SECTION II. TELECOMMUNICATION, ELECTRONICS AND NANOTECHNOLOGY
Month, Year 04, 2015 @en
Index UDC 628.003.15
DOI
Abstract The problem of an assessment and calculation of probabilities for normal distribution caused by need of a choice for such assessment from a number of the existing tabulated functions and options of use of integration limits in them is defined. For the solution of this problem the assessment is given to these functions in the beginning - "Laplace"s functions", to "classical integral of Laplace", "integral of probability (mistakes)", "Crump"s function" and "additional function of mistakes". This assessment is carried out taking into account various options of values of limits of integration in these functions. The interrelation of these functions decided on use of results of this assessment. On the basis of these interrelations ratios for definition of integrated function of the normal law of distribution through each of the above functions were found. Thus, using tabular values of any of these functions, there was an opportunity, without doing what transformations, to make calculation of probabilities for normal distribution. The purpose of this work is assistance to the scientific and engineering workers investigating and developing systems of telecommunications. Therefore in the last part of work examples of use of the received results for an assessment of one of the main characteristics of a mobile radio communication - probabilities (or shares of points in a reception place) excess of level of a radio signal over the demanded (threshold) level in a reception place with known average value of incidentally changing radio signal level are given. Also, the example for digital systems by definition of probability of an error of reception of an elementary signal (bit) at influence of pulse hindrances is given.

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Keywords Normal distribution; integrated function of distribution; distribution density; Laplace's function; Crump's function; integral of probabilities.
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