# 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 Failed to parse (unknown error): (b_1,b_2) with 2-vector mean Failed to parse (unknown error): (\mu_1,\mu_2) and 2x2 matrix covariance Failed to parse (unknown error): \Sigma . What is the distribution of Failed to parse (unknown error): b_1 given that Failed to parse (unknown error): b_2 has the particular value Failed to parse (unknown error): b_c ? In particular, what is the mean and standard deviation of the conditional distribution of Failed to parse (unknown error): 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 Failed to parse (unknown error): b_2 instead of conditioning on it.