Use the following code to generate a working dataset:

N $<-30000$

J $<-3$

pJ $<-$ c$(0\mathrm{.}1,0\mathrm{.}3,0\mathrm{.}6)$

## b has a multinomial distribution with parameters n$=1,$ p$1..$ pJ

b $<-$ t$($rmultinom$($N$,1,$pJ $))$

lambda $<-$ c$(1,2,3)$

##

Y $<-$ rexp$($N$,$ lambda$[1])*$ b$[,1]+$

rexp$($N$,$ lambda$[2])*$ b$[,2]+$

rexp$($N$,$ lambda$[3])*$ b$[,3]$

Find estimates of pj $$s and $\backslash$lambda j $$s using the EM algorithm in R