Fxy(x,y) = { (1-eαx)(1-eβy) , x ≥0 , y≥0 , α, β ≥0 , 0 for any else}?

joint probability distribution function of the random variable x, y is given by:
fxy(x,y) = { (1-eαx)(1-eβy) , x ≥0 , y≥0 , α, β ≥0 , 0 for any else}

- Prove that X and Y are independent
- find marginal distribution function for x and y
- find P[X ≤1, Y≤ 1] ,P[X≤ 1], P[Y≤ 1], and P[X >x , Y> y]