# Segment 21. Marginalize or Condition Uninteresting Fitted Parameters

## Contents

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### Problems

#### To Calculate

1. Consider a 2-dimensional multivariate normal distribution of the random variable $\displaystyle (b_1,b_2)$ with 2-vector mean $\displaystyle (\mu_1,\mu_2)$ and 2x2 matrix covariance $\displaystyle \Sigma$ . What is the distribution of $\displaystyle b_1$ given that $\displaystyle b_2$ has the particular value $\displaystyle b_c$ ? In particular, what is the mean and standard deviation of the conditional distribution of $\displaystyle b_1$ ? (Hint, either see Wikipedia "Multivariate normal distribution" for the general case, or else just work out this special case.)

2. Same, but marginalize over $\displaystyle b_2$ instead of conditioning on it.