Three zero mean, unit variance random variables X, Y, and Z are added to form a new random variable, W = X + Y + Z. Random variables X and Y are uncorrelated, X and Z have a correlation coefficient of 1/2, and Y and Z have a correlation coefficient of -1/2.
a) Find the variance of W.
b) Find the correlation coefficient between W and X.
c) Find the correlation coefficient between W and the sum of Y and Z.
This can be treated very much as a "formula" question. Note that $$\text{Var}(W)=\text{Var}(X)+\text{Var}(Y)+\text{Var}(Z)+2\text{Cov}(Y,Z)+2\text{Cov}(Z,X)+2\text{Cov}(X,Y).$$ For the covariances, recall that the correlation coefficient $\rho(U,V)$ is given by $$\rho(U,V)=\frac{\text{Cov}(U,V)}{\sqrt{\text{Var}(U)\text{Var}(V)}}.$$
Now you have all the ingredients to compute. Computation will not be hard.