y = rgamma(1000,2,1)
x = runif(1000,0,y)

par(mfrow=c(1,1))
plot(x,y)

mean(x<1 & y<2)
mean(x<1 & y<0.5)

sum(y < x^2)/1000

mean(x)
mean(y)

cov(x,y)
cor(x,y)

mean(y-x)
var(y-x)

par(mfrow=c(1,2))
plot(x,y, main="Theoretical")
lines(y=x+1, x=x, col="red")

plot(x,y, main="Lowess")
lines(lowess(x,y),col="red")