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)=?
The formula for calculating E(X+Y+Z/X) is E(X) + E(Y) + E(Z), where E(X), E(Y), and E(Z) represent the expected values of X, Y, and Z, respectively.
To calculate E(W/X+Y), you first need to calculate the joint probability distribution of W, X, and Y. Then, you can use the formula E(W/X+Y) = ∑∑∑ w * P(w,x,y) / P(x,y), where w represents the values of W, P(w,x,y) represents the joint probability of W, X, and Y, and P(x,y) represents the joint probability of X and Y.
Yes, you can use the linearity property of expected value to find E(X+Y+Z+W) by adding E(X+Y+Z/X) and E(W/X+Y).
E(X+Y+Z/X) represents the conditional expected value of X+Y+Z given X, while E(X+Y+Z)/X represents the expected value of X+Y+Z divided by X. In other words, E(X+Y+Z/X) takes into account the value of X, while E(X+Y+Z)/X does not.
To find the covariance between X+Y+Z and W, you can use the formula cov(X+Y+Z, W) = E((X+Y+Z)(W)) - E(X+Y+Z) * E(W). You can calculate the first term using E(X+Y+Z)/X and E(W/X+Y), and the second term using E(X+Y+Z/X) and E(W/X+Y), respectively.