If we have $Z_{t-1} = (X_1, \ldots,X_{t-1})$ and we know $(S_{t-1} \mid Z_{t-1}) \backsim N (\hat{S}_{t-1}, P_{t-1})$, where $S_t = G_{t}S_{t-1} + w_{t}$ and $X_{t} = F_tS_t +v_t$, so I know that $(S_t \mid Z_{t-1})$ and $X_t \mid S_t, Z_{t-1}$ both will be normal, how can I calculate mean and variance doing it using conditional expectation?
2026-04-03 10:52:20.1775213540
Conditional Expectation
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