update on typos

doc/src/week38/exercisesweek38.do.txt

@@ -39,24 +39,28 @@ Here the expected value $\mathbb{E}$ is the sample value.
 
 Show that you can rewrite  this in terms of a term which contains the variance of the model itself (the so-called variance term), a
 term which measures the deviation from the true data and the mean value of the model (the bias term) and finally the variance of the noise.
+
 That is, show that
 !bt
 \[
-\mathbb{E}\left[(\bm{y}-\bm{\tilde{y}})^2\right]=(\mathrm{Bias}[\tilde{y}])^2+\mathrm{var}[\tilde{f}]+\sigma^2, 
+\mathbb{E}\left[(\bm{y}-\bm{\tilde{y}})^2\right]=\mathrm{Bias}[y]+\mathrm{var}[\tilde{y}]+\sigma^2, 
 \]
 !et
 with 
 !bt
 \[
-(\mathrm{Bias}[\tilde{y}])^2=\left(\bm{y}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2,
+\mathrm{Bias}[y]=\mathbb{E}\left[\left(\bm{y}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right],
 \]
 !et
 and 
 !bt
 \[
-\mathrm{var}[\tilde{f}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2.
+\mathrm{var}[\tilde{y}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2.
 \]
 !et
+The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 37.
+Explain what the terms mean and discuss their interpretations.
+
 
 Explain what the terms mean and discuss their interpretations.
 
@@ -70,3 +74,5 @@ You can follow the code example in the jupyter-book at URL:"https://compphysics.
 
 
 See also the whiteboard notes from week 37 at URL:"https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf"
+
+