# Stochastics: HW 7, due Wed Apr 23

1. The Autocovariance problem posted last week..

2. Consider the random variable

and let be the event that or .

- Compute .
- Compute .
- Let be distributed like and let . Compute .
- Compute .

3. Let be a sequence of iid random variables and let . Let be the moment generating function of (and hence of each ). Fix and assume . Let and for ,

.

Define . Show that is a martingale with respect to .

In problem 2, are X and Y independent (for E[Z|X])?

That’s correct, Josh. Good catch.