| Popis: |
This chapter discusses the distribution and mean value of a random variable. A random variable x is considered given if its distribution function F ( x a ) = P ( x a ), which determines the probability, that in experiments the random variable will assume a value not exceeding the value of some real number x a , that is, it will remain within the limits — ∞ and x a . The function defined thus is called the integral distribution function or the integral distribution law. The distribution function is an abstract mathematical model with the help of which experimentally observed values may be described. One of the tasks of statistical processing of material consists in finding a distribution function which, on the one hand, would describe the observed values of the random variable sufficiently well, and on the other, would be convenient for further statistical analysis. Analytical expressions for a distribution function contain one or several constants that are called distribution parameters. Thus, for example, normal distribution has two parameters; the mathematical expectation or the mean value of the random variable and the variance. Poisson's distribution has one parameter that is identically equal to the mean value and to the variance, and so on. If one knows the distribution law of the random variable, then the variable can be completely characterized by the numerical values of the parameters. |
