Independent Exponential Functions

Question

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?

Please wrap $X$ and $Y$ with $ as they are math variables. — GNUSupporter 8964民主女神地下教會, Aug 10 '18 at 09:07
could is the best option among the 4.. You can't assert anything for sure with this much info.. but could, yeah.. could goes with everything! Cheers! — Vizag, Aug 10 '18 at 09:13
The definition of $f_{xy}$ does not make sense. A positive constant is not a density function. Do you mean that $f_{xy}$ is exponential with parameter $\lambda \alpha$?. — Kavi Rama Murthy, Aug 10 '18 at 09:13
They really ask if the PDFs are independent? This makes no sense. — Did, Aug 10 '18 at 09:15

score 0 · Accepted Answer · answered Aug 10 '18 at 09:07

0

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.

answered Aug 10 '18 at 09:07

user449911

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Independent Exponential Functions

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