Eleisha's Segment 21: Marginalize or Condition Uninteresting Parameters

To Calculate:

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

2. Same, but marginalize over $b_{2}$ instead of conditioning on it.

To Think About:

1. Why should it be called the Fisher Information Matrix? What does it have to do with "information"?

2. Go read (e.g., in Wikipedia or elsewhere) about the "Cramer-Rao bound" and be prepared to explain what it is, and what it has to do with the Fisher Information Matrix.

Back To: Eleisha Jackson