posterior distribution $\mu|\sigma^2,\boldsymbol{x}$

by Danny   Last Updated January 20, 2018 14:19 PM

I have found that

$f(\mu| \sigma^2,\boldsymbol{x}) \propto e^{\sum_{i=1}^{10} \frac{(\mu-x_i)^2}{2\cdot\sigma^2 \cdot z_i}}$

The density is proportional to the product of 10 independent ($N(x_i,\sigma^2z_i)$) gaussian random variables . but what is the distribution of $\mu|\sigma^2,\boldsymbol{x}$? The point is that I want to generate a random draw from $\mu|\sigma^2,\boldsymbol{x}$. But I don't know from which distribution?

Is it possible to deduce from the expression what distribution $\mu|\sigma^2,\boldsymbol{x}$ has

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