# Conditional and unconditional variance, autocovariance and autocorrelation of an ARMA process

Given an ARMA(1,1) process $$x_t = a + bx_{t-1} + \varepsilon_t + \theta\varepsilon_{t-1}$$, how can we

1. find the conditional variance, i.e. $$Var_{t-1}(x_t)$$,
2. find the unconditional variance, i.e. $$Var(x_t)$$,
3. find the autocovariance and autocorrelation for the lags 1 and 2?

I would appreciate a detailed answer.