6.3.1—Continuous random variables

For a continuous X, probabilities are areas over intervals: P(a≤X≤b)=∫ₐᵇf(x)dx, and P(X=x)=0 for every single point.

State the support and use a density or CDF that is non-negative and normalised. Endpoint inclusion does not change a continuous probability.

If X is uniform on [0,4], P(1<X<3)=2/4=0.5.

A density height is not a probability; only an area over a range is.