Tom's Oct 7 edits of two lectures

Author: thomassargent30

lectures/linear_models.md

@@ -556,7 +556,7 @@ information, to be defined below.
 However, you should be aware that these "unconditional" moments do depend on
 the initial distribution $N(\mu_0, \Sigma_0)$.
 
-#### Moments of the Observations
+#### Moments of the Observables
 
 Using linearity of expectations again we have
 
@@ -585,9 +585,8 @@ is not quite as good as knowing the full distribution.
 However, there are some situations where these moments alone tell us all we
 need to know.
 
-These are situations in which the mean vector and covariance matrix are **sufficient statistics** for the population distribution.
+These are situations in which the mean vector and covariance matrix are all of the  **parameters** that pin down the population distribution.
 
-(Sufficient statistics form a list of objects that characterize a population distribution)
 
 One such situation is when the vector in question is Gaussian (i.e., normally
 distributed).
@@ -753,8 +752,7 @@ The black line is the population density of $y_T$ calculated from {eq}`lss_mgs_y
 The histogram and population distribution are close, as expected.
 
 By looking at the figures and experimenting with parameters, you will gain a
-feel for how the population distribution depends on the model primitives {ref}`listed above <lss_pgs>`, as intermediated by
-the distribution's sufficient statistics.
+feel for how the population distribution depends on the model primitives {ref}`listed above <lss_pgs>`, as intermediated by the distribution's parameters.
 
 #### Ensemble Means
 

lectures/multivariate_normal.md

@@ -791,7 +791,7 @@ The solid blue line in the plot above shows $\hat{\mu}_{\theta}$
 as a function of the number of test scores that we have recorded and
 conditioned on.
 
-The blue area shows the span that comes from adding or deducing
+The blue area shows the span that comes from adding or subtracting
 $1.96 \hat{\sigma}_{\theta}$ from $\hat{\mu}_{\theta}$.
 
 Therefore, $95\%$ of the probability mass of the conditional
@@ -1875,7 +1875,7 @@ Although the  two equations are not identical, they display striking family rese
 * the second equation tells dynamics that work  **backward** in time
 * while many of the terms are similar, one equation seems to apply matrix transformations to some matrices that play similar roles in the other equation 
 
-The family resemblences of these two equations reflects a transcendent **duality** between control theory and filtering theory.
+The family resemblences of these two equations reflects a transcendent **duality** that prevails between control theory and filtering theory.
 
 ### An example