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Digital Characteristics Calculator

Calculate expectation, variance, characteristic functions, and moments for common probability distributions with detailed step-by-step solutions.

Calculator Settings
Configure parameters for digital characteristics calculation
Calculation Results
Normal Distribution N(μ, σ²) - expectation & variance results

Configure parameters and click "Calculate" to see results

Mathematical Theory
Fundamental concepts and formulas for digital characteristics

Key Formulas

Expectation
E[X]={ixip(xi)discretexf(x)dxcontinuousE[X] = \begin{cases} \sum_i x_i p(x_i) & \text{discrete} \\ \int_{-\infty}^{\infty} x f(x) dx & \text{continuous} \end{cases}
Variance
Var(X)=E[X2](E[X])2\text{Var}(X) = E[X^2] - (E[X])^2
Characteristic Function
fX(t)=E[eitX]=eitxdF(x)f_X(t) = E[e^{itX}] = \int_{-\infty}^{\infty} e^{itx} dF(x)
Related Resources
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