Question

show that the following random variables X1 and X2 with the joint pdf are independent

Answer 1

\[f(x_1,x_2)=12x_1x_2(1-x_2) \] for 0<x1<1, 0<x2<1

Answer 2

where are you stuck?

Answer 3

how should i prove it? i know that the region is good because it doesn't depend on each other, but how to use the formula to prove it or other way

Answer 4

show that

\[f_{X_1,X_2}(x_1,x_2)=f_{X_1}(x_1)f_{X_2}(x_2)\]

Answer 5

so do the marginals of both fx and then multiply them and if i get the same thing then they are independent?

Answer 6

http://en.wikipedia.org/wiki/Independence_%28probability_theory%29#Two_random_variables