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I'm having trouble with a few multinomial questions. I know that for a multinomial distribution we have:

$$p_1+p_2+\dots+p_k=1$$ $$X_1+X_2+\dots+X_k=n$$

For $(X_1,\dots,X_{10}) ∼$ Mult$(n,p_1,··· ,p_{10})$ I need show that:

  1. $X_1$ ~ $Bi(n,p_1)$

  2. $f_{X_1, X_2}(x_1,x_2)= \frac{n!}{x_1!x_2!(n-x_1-x_2)!}p_1^{x_1}p_2^{x_2}(1−p_1−p_2 )^{n−x1−x2}I(n−x_1−x_2)$

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