Bayesian updating normal distribution
You will learn to use Bayes’ rule to transform prior probabilities into posterior probabilities, and be introduced to the underlying theory and perspective of the Bayesian paradigm.For $X_, X_,..., X_$ iid $\mathcal(\theta,\sigma^2)$, and a priori distribution $\theta\sim\mathcal(\mu,\tau^2)$, you should obtain posteriori distribution $\mathcal(\mu_,\tau^2_)$, where: $$\mu_=\frac\quad\text\quad\tau^_=\left(\frac \frac\right)^$$ As for the Bayesian estimator  well, I believe that that would depend on your risk function; with a MSE function, you should obtain $\theta^_=\mu_$.Suppose we observe one draw from the random variable $X$, which is distributed with normal distribution $\mathcal(\mu,\sigma^2)$. (Interpretation: we get noisy signals about $\mu$, which are known to be normally distributed with known variancethis is the draw of $X$.Here is a tenminute overview of the fundamental idea. But there's a catch: Sometimes the arithmetic can be nasty.
On your way to the hotel you discover that the National Basketball Player's Association is having a convention in town and the official hotel is the one where you are to stay, and furthermore, they have reserved all the rooms but yours.
I have to calculate the posteriori distribution on $\theta$ and the Bayes estimator.
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