Continuous Random Variables (VCE SSCE Mathematical Methods): Flashcards

Variable that can take any value within a specific interval

Continuous: any value in range; Discrete: specific separated values

$\Pr(X = x) = 0$ for all $x$

Function representing probability distribution of continuous variable

$f(x) \geq 0$ for all $x$ (always non-negative)

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

As areas under the PDF curve

$\Pr(a < X < b) = \int_a^b f(x) \, dx$

Yes, $f(x)$ values are not probabilities themselves

$\Pr(a < X < b) = \Pr(a \leq X \leq b)$ (endpoints don't matter)