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 $\theta$. (d) Use the data on the haptoglobin type and compute the MLE $\hat{\theta}