MATHEMATICAL EXPECTATIONS OF FUNCTIONS FROM RANDOM SUMS

A random sum is the sum of a random number of random variables. Instead of adding a fixed number of terms, the number of terms itself is uncertain. This structure appears naturally in many applied probability models. The main problem studied in this topic is how to compute or analyze the expected value of a function of such a random sum. This is more complicated than finding the expectation of a simple random variable because two layers of randomness are involved: randomness in the number of terms, randomness in the terms themselves.