Calculating E(X+Y+Z/X) and E(W/X+Y)

[ParisSpart]

we throw three ordinary dice and X,Y,Z their results and W=X+Y+Z how many differents values have the random values E(W/X) and E(W/X+Y)?

can anyone explain me how to beggin because i am confused.. i will use E(X+Y+Z/X)=E(X/X)+E(Y/X)+E(Z/X)=? for the first one?

 

[HallsofIvy]

we throw three ordinary dice and X,Y,Z their results and W=X+Y+Z how many differents values have the random values E(W/X) and E(W/X+Y)?

can anyone explain me how to beggin because i am confused.. i will use E(X+Y+Z/X)=E(X/X)+E(Y/X)+E(Z/X)=? for the first one?

I think you need to go back and look at the problem again. I don't know what you mean by "how many differents values have the random values E(W/X) and E(W/X+Y)?"
How many different values" of what? E(W/X) and E(W/(X+ Y) are specific numbers. Do you mean how many (X, Y, Z) combinations give W that are equal to those expectations. Actually, I would be surprized if those were integer values. Or do you mean simply "find E(W/X) and E(W/(X+Y))"?

It's not all that difficult to determine the $6^3= 216$ combinations of three dice. W ranges in value from 3 to 18.

 

[haruspex]

E(X+Y+Z/X)=E(X/X)+E(Y/X)+E(Z/X)=?

Assuming you mean E((X+Y+Z)/X), that's a good start. E(X/X) is obvious. Since X and Y are independent, can you expand E(Y/X) into separate functions of X and Y?