Suppose random variables X and Y have the following joint probability function

[dazhebhs]

Suppose random variables X and Y have the following joint probability function. Show that X and Y are not independent of each other, but the following relationship holds.

E(XY)=E(X) E(Y)

 

[stapel]

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please be complete, in accordance with the "Read Before Posting" thread pinned at the top of this forum. Thank you!

Eliz.

 

[lookagain]

I reported the above post for repeated abuse of posting problems without work.
It is better to act on this early instead of the problem dragging along and repeating
ourselves with uncooperative new users.

 

[Dr.Peterson]

It's worth pointing out that this user submitted all four questions within about half an hour, and before getting any direct requests to show work. Also, there is likely a language barrier. So I wouldn't yet use the label "uncooperative". That may come later ...