Probability

The Analysis of Data, volume 1

Random Processes: Exercises

6.8. Exercises

1. Describe a collection of finite dimensional marginals that violates the consistency conditions.
2. Prove formally that the marginals defining the iid process satisfy the consistency conditions.
3. Prove that the random walk process $\mathcal{Z}$ has one dimensional binomial marginals.
4. Consider a discrete-time random walk model similar to the on in this chapter, with the following exception: the walker steps two steps forward with probability $\theta$ and one step backwards with probability $1-\theta$. Characterize the process in terms of the RP categories (stationary, Markov, etc.), and derive its expectation, variance, and autocorrelation functions.