update week37

doc/src/week37/week37.do.txt

@@ -747,10 +747,7 @@ is a normal distribution whose mean is the
 mean value of the PDF $p(x)$ and whose variance is the variance
 of the PDF $p(x)$ divided by $m$, the number of values used to compute $z$.
 
-The theorem is satisfied by a large class of PDFs. Note however that for a
-finite $m$, it is not always possible to find a closed expression for
-$\tilde{p}(x)$.
-The central limit theorem leads then to the well-known expression for the
+The central limit theorem leads to the well-known expression for the
 standard deviation, given by 
 
 !bt
@@ -771,12 +768,24 @@ the familiar expression in statistics
 !et
 
 In many cases however the above estimate for the standard deviation,
-in particular if correlations are strong, may be too simplistic.
+in particular if correlations are strong, may be too simplistic. Keep
+in mind that we have assumed that the variables $x$ are independent
+and identically distributed. This is obviously not always the
+case. For example, the random numbers (or better pseudorandom numbers)
+we generate in various calculations do always exhibit some
+correlations.
+
+
+
+The theorem is satisfied by a large class of PDFs. Note however that for a
+finite $m$, it is not always possible to find a closed form /analytic expression for
+$\tilde{p}(x)$.
+
 
 !split
 ===== Confidence Intervals =====
 
-Confidence intervals are used in statistics is a type of estimate
+Confidence intervals are used in statistics and represent a type of estimate
 computed from the observed data. This gives a range of values for an
 unknown parameter such as the parameters $\bm{\beta}$ from linear regression.