Solution
= Solution
Using the <EM for merged multinomial cells> E-step,
$$
z^{(t)}=\frac{2(125)}{2+0.5}=100,\qquad
\boxed{y_3^{(t)}=125-100=25.}
$$
Applying the M-step <maximum-likelihood estimator> to the filled counts gives
$$
\boxed{\theta^{(t+1)}=\frac{34+25}{38+34+25}=\frac{59}{97}\approx0.6082474227.}
$$