h<-function(x){
x
}

draws <- rt(10000,df=1)
wh <- h(draws)*g(draws)/dt(draws,df=1)
w <- g(draws)/dt(draws,df=1)


numerator <- mean(wh)
denominator <- mean(w)
expectation <- numerator/denominator

c(numerator, denominator, expectation)


xx<-seq(-3,6,length=100)
plot(xx,g(xx),type="l",col="red",lwd=4)
lines(xx,dt(xx,df=1),col="black",lwd=4)
legend(3,1,legend=c("I()","g()"),col=c("black","red"),lwd=4)