Random variables, their types

The mathematical statistics is the science, engaged methods of processing of experimental data. Any science solves in ascending order complexity and importance the following problems:

1) phenomenon description;

2) analysis and forecast;

3) search of optimum decision.

Such problems are solved also with mathematical statistics:

1) to systematize the received statistical material;

2) on a basis of the received experimental data to estimate numerical characteristics of an observable random variable interesting us;

3) to define number of experiences, sufficient for reception of authentic results at the minimal mistakes of measurement.

One of problems of the third type is the problem of check of credibility of hypotheses. It can be formulated as follows: there is a set of the skilled data concerning one or several random variables. It is necessary to define, whether these data contradict this or that hypothesis, for example, to a hypothesis that the investigated random variable is distributed according to the certain law, or two random variables are not correlated (i.e. are not connected among themselves), etc. As a result of check of credibility of hypothesis either it is rejected, as contradicting skilled data, or is accepted as comprehensible.

Thus, mathematical statistics helps experimenter to understand better the received skilled data, to estimate, are significant or not the certain observed facts, to accept or reject those or other hypotheses about the nature of the considered phenomenon.

A random variable is a variable that assumes numerical values associated with the random outcomes of an experiment, where one (and only one) numerical value is assigned to each sample point.

For example define the random variable X as the number of heads in 2 tosses of a fair, 50-50 coin. The sample space is the corresponding outcomes in this sample space get associated with values of the random variable X as because the outcomes have 1,2,1, and 0 heads respectively.

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