The discussion focuses on calculating the expected values E(W/X) and E(W/(X+Y)) where W is defined as the sum of the results from three ordinary dice rolls (X, Y, Z). Participants clarify the need to determine how many different combinations of (X, Y, Z) yield specific expected values. The total combinations of three dice rolls amount to 216, and the range of W spans from 3 to 18. The conversation emphasizes the importance of correctly interpreting the expected value calculations and the independence of the variables involved.
PREREQUISITESStudents and professionals in statistics, probability theorists, and anyone interested in understanding the behavior of random variables in dice games.
ParisSpart said: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?
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?ParisSpart said:E(X+Y+Z/X)=E(X/X)+E(Y/X)+E(Z/X)=?