I first want to confirm whether or not if the integral of the following PDF for two joint uniform distributions is equal to 1 for 0 < c < 1: $$∫_{0}^1 ∫_{max(0, x-1+c)}^{min(1, x+1-c)} \frac{1}{1-c^2}dydx = 1$$
If this is the case, then how can I evaluate the expected value of the products between the two random variables?
$$E[XY] = ∫_{0}^1 ∫_{max(0, x-1+c)}^{min(1, x+1-c)} \frac{xy}{1-c^2}dydx$$