>>357
pr(x_i, y_j, z_k|u_m)=pr(x_i, y_j, z_k,w_1|u_m)+pr(x_i, y_j, z_k,w_1|u_m)
=pr(x_i|u_m)pr(y_j|u_m)pr(z_k|u_m)pr(w_1|u_m)+pr(x_i|u_m)pr(y_j|u_m)pr(z_k|u_m)pr(w_2|u_m)
=pr(x_i|u_m)pr(y_j|u_m)pr(z_k|u_m) ∵pr(w_1|u_m)+pr(w_2|u_m)=1

同様に
pr(x_i, y_j|u_m)=pr(x_i|u_m)pr(y_j|u_m)

また
pr(x_i, y_j)=pr(x_i, y_j,u_1)+pr(x_i, y_j,u_2)=pr(x_i, y_j|u_1)pr(u_1)+pr(x_i, y_j|u_2)pr(u_2)

流れとしてはこんな感じ