I will have a Statistics course soon, so I decided to start a Probability Theory class myself and learn the "basics" first before I start the statistics. I reached the chapter Conditioning on Random Variable's and there was this question I find very difficult to solve. The question is;
Let X and Y be independent, continuous random variables with expected value and variance µX,σ2 X and respectively µY ,σ2 Y . Determine/ Calculate; E[(X + Y )X |Y ].
I know how to integrate over already probability density functions and then calculate the value's, but with the conditioning on a stochastic it becomes increasingly more difficult! Could someone help me out or give me any hints?