4.1.4—PDF and CDF

Once F is known, P(a<X≤b)=F(b)−F(a), P(X>b)=1−F(b), and quantiles are found by solving F(x)=p. Endpoints do not matter for continuous distributions.

State the support before evaluating a CDF. If a piecewise formula is given, use the correct branch and check continuity at the join.

If F(x)=x² on 0≤x≤1, then P(0.2<X≤0.8)=0.64−0.04=0.60; the density is not needed for this subtraction.

F(b)−F(a) is not F(b−a), and a CDF value is cumulative probability, not a density height.