Consider the H$^($MM$)$ chnimen holnin,

The prior probability P$($x$\_(0)),$ dynamics model P$($x$\_($t$+1)|$x$\_($t$)),$ and sensor model P$($E$\_($t$)|$x$\_($t$))$

are as follows:

We perform a first dynamics update, and fill in the resulting belief distribution B$^(\text{'})($x$\_(1)).$

We incorporate the evidence E$\_(1)=$c$.$ We fill in the evidence$-$weighted distribution

P$($E$\_(1)=$c$|$x$\_(1))$B$^(\text{'})($x$\_(1)),$ and the $($normalized$)$ belief distribution B$($x$\_(1)).$

You get to perform the second dynamics update. Fill in the resulting belief distribution

B$^(\text{'})($x$\_(2)).$

B$^(\text{'})($x$\_(2)=0)$

B$^(\text{'})($x$\_(2)=1)$

Now incorporate the evidence E$\_(2)=$c$.$ Fill in the evidence$-$weighted distribution

P$($E$\_(2)=$c$|$x$\_(2))$B$^(\text{'})($x$\_(2)),$ and the $($normalized$)$ belief distribution B$($x$\_(2)).$

P$($E$\_(2)=$c$|$x$\_(2))$B$^(\text{'})($x$\_(2))$ when x$\_(2)=0$

P$($E$\_(2)=$c$|$x$\_(2))$B$^(\text{'})($x$\_(2))$ when x$\_(2)=1$

B$($x$\_(2)=0)$

B$($x$\_(2)=1)$