Consider a regular continuous time Markov chain X_t on {0, 1} with rates q_(0,1) = q_(1,0) = > 0. Assume that P(X_0 = 0) = P(X_0 = 1). Define {S_n, n 1} to be the successive return times to 0 for t > 0.

1. Find the transition function.

2. What is the expected amount of time until the first jump?

3. Calculate E(S_1).

4. Calculate Cov(S_1, S_2).