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Der Erwartungswert einer Zufallsgröße kann generell am Graphen ihrer Verteilungsfunktion durch eine naheliegende Gleichheit zweier Flächeninhalte festgelegt werden. Äquivalent dazu lässt er sich mit zwei uneigentlichen Riemann-Integralen darstellen. Davon ausgehend werden die Tschebyschow-Ungleichung und ihre Modifikation mit strikten Ungleichheitszeichen hergeleitet.
Glass-ceramic composites consisting of potassium-iron-silicate glass and barium titanate mixed in various proportions were successfully synthesized by low-temperature sintering. The crystal structure of the obtained composite samples, the porosity and the microhardness were studied by the X-ray diffraction, the electron microscopy, the weight method, and the Vickers method. Electrical characteristics (dielectric permittivity, tunability and losses) of as-prepared and annealed in oxygen medium samples were investigated at microwaves. According to structural analysis, the synthesized samples are a mixture of KFeSi glass, ferroelectric BaTiO3, and dielectric barium polytitanates; the ratio of the latter determines the electrical properties of the composites. Depending on the content of barium titanate, the studied composite samples show a permittivity from 50 to 270 with a dielectric loss level of 0,1–0,02 in frequency range from 3 to 10 GHz. Annealing of composite samples in an oxygen-containing environment leads to an increase in their dielectric permittivity and tunability by 10–25% and a twofold decrease in dielectric loss.