请教一道关于contour plot的问题

肉肉

The random variables X and Y are independent and identically distributed with normal mixture distribution.  The components of the mixture have N(0,1) and N(3,1) distributions with mixing probabilities p1 and p2=1-p1 respectively.  Generate a bivariate random sample from the joint distribution of (X,Y) and construct a contour plot.  Adjust the levels of the contours so that the contours of the second mode are visible.
请问这道题应该怎么做？

chunfei_xu

题目是英文，所以根据猜测来尝试回答：
设P1为0.2,P2为0.8
U<-c(-10：10)
V<-U
Fx<-0.2*dnorm(U,0,1)+0.8*dnorm(V,3,1)
Fy<-0.2*dnorm(U,0,1)+0.8*dnorm(V,3,1)   
Fxy<-tcrossprod(Fx,Fy)     
contour(U, V, Fxy, nlevels = 15)
最后悔画出一个等高图，但是否正确还请自己确定。本问题涉及到概率这个数学问题，有点超出了本人的能力。