Mean and Variance of a Distribution (HSC SSCE Mathematics Advanced): Flashcards

Discrete: $\sum$; Continuous: $\int$

$E(X) = \int_a^b xf(x) \, dx$

The balancing point/average value

How spread out the distribution is

$\int_a^b (x - \mu)^2 f(x)\,dx$

$\int_a^b x^2 f(x)\,dx - \mu^2$

Method 2 - simpler algebra

$\sigma = \sqrt{\text{Var}(X)}$

SD: same as variable; Variance: squared units

Both give exactly the same answer