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I'm having trouble finding an expression for the function:

$$f_{X_1+X_2,X_2+X_3|X_2+X_4}(·,·|t)$$

The notation is a little confusing for me but I know that $(X_1,··· ,X_{10})$ follows a multinomial distribution. If anyone could help me out that would be fantastic.

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For every random variables $(U,V,T)$, $$f_{U,V\mid T}(u,v\mid t)=\frac{f_{U,V,T}(u,v,t)}{f_{T}(t)}$$ You might wish to explain which term on the RHS you fail to compute when $U=X_1+X_2$, $V=X_2+X_3$, $T=X_2+X_4$.

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