Simplifying a multivariate random variable

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$(Y_1,Y_2,Y_3,Y_4)$ is $Multi(n,\theta_1,\theta_2,\theta_3,\theta_4)-distributed. $

I want to simplify the expression for the vector $(X_1,X_2)$, where $X_1=Y_1+Y_2$ and $X_2=Y_3+Y_4$.

Is the simplification related to the pmf of $X_1$ and $X_2$ or?