Conditional expectation, also known as conditional mathematical expectation. For convenience, we discuss the case of two random variables ξ and ξ, assuming that they have a density function p(x, y), and note that the conditional density function of ξ has p(y∣x) and the density function of ξ has p 1(x). Defined under the condition of ξ = x, the conditional mathematical expectation of ξ is defined as: e {ξ ξ = x} = ∫ YF (y ∣ x) dy.