Suppose $T = Y_{1} + Y_{2} + Y_{3}$ where $Y_{i}$ is a random variable. Let $U = Y_{1} + Y_{3} - Y_{4}$.
$T$ and $U$ are not independent.
How could I make a formula to find Covariance$[T,U]$ if Cov$[Y_{3}, Y_{i}] = p$, and the rest of the $Y_{i}$'s are independent.
Note that $\operatorname{Cov}$ is linear in each argument (i.e. $\operatorname{Cov}(aX+bY,Z)=a\operatorname{Cov}(X,Z) + b\operatorname{Cov}(Y,Z)$, and similarly for the second argument) and $\operatorname{Cov}(X,X) = \operatorname{Var}(X)$. Using this, you should be able to expand $\operatorname{Cov}(T,U)$, then use the known covariance between each $Y_i$.