Let Pt be a random walk with increment E t , and let E t be i. normal with mean u and variance sigma 2 . Assume t 0 = 1. Derive the unconditional...

Let Pt be a random walk with increment Et, and let Et be i.i.d. normal with mean u and variance sigma2. Assume t0 = 1.

1. Derive the unconditional mean and variance of Pt.

2. Derive the conditional mean and variance of Pt given a value of Pt-1 = x.

3. Compare and contrast the behavior of the unconditional and conditional variance, as t --infinity .