4.13 For the situation of Example 4.10:

(a) Show that the M-step of the EM algorithm is given by

µˆ =



4 i=1 ni j=1 yij + z1 + z2

/12,

αˆi =



2 j=1 yij + zi

/3 − ˆµ, i = 1, 3

=



3 j=1 yij

/3 − ˆµ, i = 2, 4.

(b) Show that the E-step of the EM algorithm is given by zi = E Yi3|µ = µ, α ˆ i = αˆi

!

= µˆ + αˆi i = 1, 3