Математическое ожидание. Created by dermeco1. matematika-ru

Математическое ожидание...

dermeco1 @dermeco1

July 2022 1 4 Report

Математическое ожидание

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NNNLLL54

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$F(x)=\left\{\begin{array}{lll}0\; ,\; x\leq 0\\\frac{x^2}{49}\; ,\; 07\end{array}\right\\\\\\f(x)=F'(x)=\left\{\begin{array}{lll}0\; ,\; x\leq 0\\\frac{2x}{49}\; ,\; 07\end{array}\right$

$M(X)=\int\limits^{+\infty }_{-\infty }\, x\cdot f(x)\, dx\\\\M(X)=\int\limits^0_{-\infty }\, 0\cdot dx+\int\limits^7_0\, x\cdot \frac{2x}{49}\, dx+\int\limits^{+\infty }_7\, 0\cdot dx=\\\\=\frac{2}{49}\cdot \int\limits^7_0\, x^2\, dx=\frac{2}{49}\cdot \frac{x^3}{3}\Big |_0^7=\frac{2}{49\cdot 3}\cdot 343=\frac{14}{3}\approx 4,67$

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