Continuous Distributions 1 (AQA A-Level Further Maths): Flashcards

Probability distribution function

$\int_{a}^{b} f(x)\,dx$

$f(x) \geq 0$ (non-negativity)

$\int_{-\infty}^{+\infty} f(x)\,dx = 1$

$\int_{-\infty}^{M} f(x)\,dx = \frac{1}{2}$

Where pdf reaches its maximum value

$\int_{-\infty}^{+\infty} xf(x)\,dx$

$E(X^2) - \mu^2$

$aE(X) + b$

$a^2\text{Var}(X)$