Expectation and variance of continuous random variables If X is a continuous random variable having probability density function f(x),then as f(x)dk≈P{x≤X≤x+dx}for dx smal Define the expected value of X by E(X)=xf(x)dx. Expectation and variance of continuous random variables ( ), ( ) { } If X is a continuous random variable having probability density function f x then as f x dx P x X x dx for dx smal ≈ ≤ ≤+ ( ) () . Define the expected value of X by E X xf x dx ∞ −∞ = ∫