Let \(Z_n\) be a collection of independent random variables with \(P(Z_n=1)=\frac12\) and \(P(Z_n=\frac12)=\frac12\) . Define \(X_0=1\) and \(X_{n+1}=Z_n X_n\).

- What is \(E( X_n | X_{n-1})\) ?
- What is \(E(X_n)\) ?
- What is \(\mathrm{Cov}(X_n,X_{n-1})\) ?