I've been staring at this for hours. Any hints?(adsbygoogle = window.adsbygoogle || []).push({});

Let the vector [tex]Y = (Y_1,Y_2,\dots,Y_k)[/tex] have a multinomial distribution with parametersnand [tex]\pi = (\pi_1,\pi_2,\dots,\pi_k)[/tex]:

[tex]\sum_{i=1}^{k}Y_i = n, \quad \sum_{i=1}^{k}\pi_i = 1[/tex]

Show that the conditional distribution of [tex]Y_1[/tex] given [tex]Y_1+Y_2=m[/tex] is binomial withn = mand [tex]\pi = \frac{\pi_1}{\pi_1+\pi_2}[/tex].

I've tried to apply the definition of a conditional probability and sum over the relevant events in the multinomial distribution, but it gives me nothing.

Thanks.

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# Homework Help: Conditional distribution

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