Could anyone please be able to help me with the following question:
We have $ \ f_{x} (x) = e^{λ} \ $ and $ \ f_{y} (y) = e^{α} \ $
If the joint PDF is equal to:
$\>$ $\>$ $\>$ $\>$
$
\ f_{xy} (x,y) = e^{λα} \
$
Then:
$\>$ $\>$ $\>$ $\>$ $ \ X \ $ and $ \ Y \ $: $\>$ $\square$ are independent ?
$\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\square$ must be independent?
$\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\square$ could be independent?
$\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\>$ $\square$ cannot be independent?
could, because we don't know how the experiment where they come from work. They could be independent and they could be not, we dont have any information about that.