Two steps of the Hamilton filter by hand

Use the model of the 13.5 worked example ($\mu = (0.05, -0.10)$, $\sigma = (0.7, 2.0)$ in percent, $p_{00} = 0.98$, $p_{11} = 0.95$). Yesterday's filtered probabilities were $(0.9, 0.1)$. The next two daily returns are $-2.5\%$ and $-1.8\%$. (a) Compute the predicted and filtered probabilities for both days and the log-likelihood contribution of the two days. (b) Compute the smoothed probability of the stressed regime on the first day, given both days. (c) Which of the numbers in (a) and (b) could a trader have used at the close of the first day?