Hi, we have X and Y as real-valued random variables and g and h as real-valued functions.

Could someone help me with the following? What is the definition of the following?

\(\displaystyle \color{red}{\text{It is in your last jpg}}\)

and

I am also required to prove the following rule of iterated expectations:

\(\displaystyle \color{red}{\text{You can find the proof here: (scroll down to iterated expectation)}}\)

Expected value - Wikipedia, the free encyclopedia
Help please and thanks in advance!