Let U=min(X,Y) and V=max(X,Y), where X and Y are independent R(0,1) random variables.
1. Compute the cdf's (cumulative dist. function) F(u) and F(v) and hence derive the pdf's (probability density function) f(u) and f(v) of the random variables U and V respectively.
2. Compute the joint cdf F(u,v) ], 0<=u<=v<=1, of the bivariate random variable (U,V) and use it to derive the pdf f(u,v).
3. Are the random variables U and V independent? Why?
Please help me! Thanks!