Let X1, X2,... be i.i.d. r.v.s with mean 0, and let Sn = X1 + + Xn. As shown in Example 9.3.6, the expected value of the first term given the sum of the first n terms is E(X1|Sn) = Sn n . Generalize this result by finding E(Sk|Sn) for all positive integers k and n.

Intro: What is Statistics • Statistics are used to determine the true state of nature and to make informed decisions that are in your best interest • We live in an age of information, or overabundant data o Data is NOT information o Data needs to be quantified to be understood as information (in statistics) o Statistics is the science of transforming...