In probability theory, Wald's equation (or Wald's identity) is an important identity that simplifies the calculation of the expected value of the sum of a random number of random quantities. In its simplest form, it relates the expectation of a sum of randomly many finite-mean, identically distributed random variables to the expected number of terms in the sum and the random variables' common expectation under the condition that the number of terms in the sum is independent of the summands.
Clearly, assumptions (1) and (2) are needed to formulate Wald's equation. Assumption (3) controls the amount of dependence allowed between the sequence... Read More