Central tendency and dispersion measures for continuous random variables

The mode of a continuous random variable is the maximum of it’s density-function

For the p-quantile it holds that \(F(\tilde{x}_p) = P(X \le \tilde{x}_p)\) and \(P(X \ge \tilde{x}_p) = 1 - p\) If the distribution function 𝐹𝐹 is strictly monotonically increasing, p-quantiles and median are unique

The expected value of a continuous random variable X with density f is given by \(\mu = E(X) = \int_{-\infty}^{\infty} x* f(x) \; dx\)

The variance of a continuous random variable X with density f is given by \(o^2 = Var(X) = \int_{-\infty}^{\infty} (x - \mu)^2 f(x) \; dx = E(X^2) - E(X)^2\)

The standard deviation of a continuous random variable X is than given by \(+\sqrt(Var(X))\)

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