# Conditional Distribuiton

by Jackson Maike   Last Updated September 12, 2019 02:19 AM

When trying to solve the following question I have to take into account the dependency of $$\alpha_2$$ to $$b_1$$, $$b_2$$ and $$S$$? Since, apparently, $$\alpha_1$$ only depends on $$\theta_1$$ e $$\theta_2$$. Any suggestions for resolution? Thanks in advance.

Let $$S \sim N(\mu, \Sigma)$$ $$b_i \sim Bern(1 - \omega)$$ $$\theta_i \sim U(-20,40)$$ Regard $$\Sigma_{ii} = 1$$ and $$\Sigma_{ij} = \rho, i \neq j$$.

For $$\alpha_1 = 0.7\theta_1 + 0.7\theta_2$$ $$\alpha_1 = 0.7\theta_1 - 0.7\theta_2$$

Find the conditional distribution of $$\alpha_1 | \alpha_2, b_1, b_2, S$$

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