5.14 The log-likelihood for a model which is a mixture of two univariate normal pdfs has the form: () = n i=1 log{(xi|1, 1) +

5.14 The log-likelihood for a model which is a mixture of two univariate normal pdfs has the form:

(ψ) = n i=1 log{αφ(xi|μ1, σ1) + (1 − α)φ(xi|μ2, σ2)}, using a self-explanatory notation. We wish to fit this model using the EM algorithm.

Let n(m)

j = n i=1 wij (ψ(m)

) for j = 1, 2.

Show that