In the factor analysis model,

X $\backslash$mu $=$ LF $+$ U$,$

where we assume that F and U are normal with E$($FF$)=$ I. Suppose we

make N i$.$i$.$d observations on X$.$

$($a$)$ Use the EM algorithm to find the MLE of L and $\backslash$Psi $.$ Hint: write down the

E$-$step and the M$-$step; the M$-$step provides updated values of the parameters.

$($b$)$ Write a computer program to implement your algorithm in R software.