Here we look at an important concept that is an extension from Bayes Theorem, which we discussed briefly.

The *condition expectation identity* says

The *condition variance identity* says

Here both and are both functions of Y and are therefore random variables themselves.

With this, we start by considering a random sum of random variables. Let where ‘s are IID with mean and variance , where is also a random variable, independent of ‘s.

Review of Basic Probability – The Culture[…] Conditional Expectations and Variances – The Culture on Continuous Random Variables […]

Introduction to Brownian Motion – The Culture[…] Review of Basic Probability – The Culture on Conditional Expectations and Variances […]