Mean & Variance Calculator

Continuous Random Variable

Mean (Expectation):
E[X] = ∫_a^b x f(x) dx

Second Moment:
E[X²] = ∫_a^b x² f(x) dx

Variance:
Var(X) = E[X²] − (E[X])²

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Mean & Variance Calculator (Continuous PDF)

Enter the PDF f(x) using JavaScript syntax (use x).

Lower limit (a):

Upper limit (b):

PDF f(x):

Discrete Random Variable

Mean (Expectation):
E[X] = ∑ x_i p_i

Second Moment:
E[X²] = ∑ x_i² p_i

Variance:
Var(X) = E[X²] − (E[X])²

Mean & Variance Calculator (Discrete PMF)

Enter values separated by commas.

Values of X:
-1, 0, 2
Probabilities P(X):
0.2, 0.3, 0.5