g <- function(x){
exp(-.5*(x^2))+.5*exp(-.5*((x-3)^2))
}

vals <- rt(10000,df=1)
w <- g(vals)/dt(vals,df=1)
q <- w/sum(w)


out <- sample(vals,size=3002,replace=T,prob=q)

mean(out)
sqrt(var(out))
mean((out<0))

xx<-seq(-3,6,length=100)
hist(out,nclass=50,prob=T,xlab="")
lines(density(out),lwd=4,col="blue")
lines(xx,.67*dnorm(xx,0,1)+.33*dnorm(xx,3,1),lwd=4,col="red")