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Thus, $left(n_{1}, n_{2}, n_{3} ight)^{T}$ is multinomial with parameters $n$ and $(1-theta)^{2}, 2 theta(1-theta)$ and $theta^{2}$. (a) Write down the likelihood function $L(theta)$ of $theta$.

Thus, $\left(n_{1}, n_{2}, n_{3} ight)^{T}$ is multinomial with parameters $n$ and $(1-\theta)^{2}, 2 \theta(1-\theta)$ and $\theta^{2}$. (a) Write down the likelihood function $L(\theta)$ of $\theta$. (b) Assume that the prior for $\theta$ is uniform between 0 and 1. Find the posterior distribution of $\theta$ given data $n_{1}, n_{2}$ and $n_{3}$. Is this a known distribution? (c) Find the Jeffrey's prior for $\theta$

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