[R] Questions about EM algorithm

[Hung-Hsuan Chen (Sean)]

Dear all:
Assume I have 3 distributions, x1, x2, and x3.
x1 ~ normal(mu1, sd1)
x2 ~ normal(mu2, sd2)
x3 ~ normal(mu3, sd3)
y1 = x1 + x2
y2 = x1 + x3

Now that the data I can observed is only y1 and y2. It is
easy to estimate (mu1+m2), (mu1+mu3), (sd1^2+sd2^2) and
(sd1^2+sd3^2) by EM algorithm since
y1 ~ normal(mu1+mu2, sqrt(sd1^2+sd2^2)) and
y2 ~ normal(mu1+mu3, sqrt(sd1^2+sd3^2))

However, I want to estimate mu1, mu2, mu3, sd1, sd2, and sd3.
Is it possible to do so by EM algorithm (or any other estimation
methods like gibbs sampling or MLE) ?

Anyone can give me some sample code or suggestions? Thanks a
lot in advance.