Continuous r.v.and PDFs A random variable X is called continuous if there is a functionfx>0, called the probability density function of X,or PDF,s.t. P(X E B)=fx(x)dx for every subset B≤R. In particular,when B [a,b], P(a≤X≤b)=fx(x)dx is the area under the graph of PDF.Continuous r.v. and PDFs • A random variable 𝑋 is called continuous if there is a function 𝑓𝑋 ≥ 0, called the probability density function of 𝑋, or PDF, s.t. 𝑃(𝑋 ∈ 𝐵) = න 𝐵 𝑓𝑋 𝑥 𝑑𝑥 for every subset 𝐵 ⊆ ℝ. • In particular, when 𝐵 = [𝑎, 𝑏], 𝑃(𝑎 ≤ 𝑋 ≤ 𝑏) = න 𝑎 𝑏 𝑓𝑋 𝑥 𝑑𝑥 is the area under the graph of PDF. 3