Continuous Distribution

A model used to describe data that can take any value within a range, often with decimal precision.

Population parameters

Mean

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

Variance

$$\sigma^2 = \int_{-\infty}^{\infty} (x - \mu)^2 f(x) \, dx$$

Covariance

$$\mathrm{Cov}(X, Y) = \int_{-\infty}^\infty \int_{-\infty}^\infty (x - \mu_X)(y - \mu_Y) f(x,y) \, \text{d}x \, \text{d}y$$

Skewness

$$\gamma_1 = \frac{1}{\sigma^3} \int_{-\infty}^\infty (x - \mu)^3 f(x) \, dx$$

Sample statistics

The collected data points from a continuous distribution are finite and discrete samples, which makes it discrete. Sample parameters of a discrete distribution is used here.