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∈B)=x(x)d for every subset B∈R. PDF fx(z) Sample space Event (as Xsb} 7Continuous 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. 7