[simulations] added exercise randomnumbers

simulations/code/normaldata.m

@@ -1,8 +1,3 @@
-% getting familiar with the randn() function:
-randn(1, 3)
-randn(3, 1)
-randn(2, 4)
-
 % simulate tiger weights:
 mu = 220.0;       % mean and ...
 sigma = 40.0;     % ... standard deviation of the tigers in kg

simulations/code/normaldata.out

@@ -1,21 +1,5 @@
 >> normaldata
 
-ans =
-
-  -0.89120   1.19863   0.95487
-
-ans =
-
-  -1.10001
-   0.79473
-   0.85979
-
-ans =
-
-  -1.19206   0.58278   1.70286  -1.28122
-  -0.19966  -1.85623   0.17962  -0.19272
-
-
 n=100:
   m=218kg, std= 39kg
   m=223kg, std= 39kg

simulations/code/randomnumbers.m

@@ -0,0 +1,17 @@
+% getting familiar with the rand() function:
+rand(1, 3)
+rand(3, 1)
+rand(2, 4)
+
+% three times the same sequence of 10 random numbers:
+n = 10;
+for k = 1:3
+    rand(1, n)
+end
+
+% serial corraltion at lag 1:
+n = 10000;
+x = rand(n, 1);
+r1 = corr(x(1:end-1), x(2:end));
+fprintf('correlation between subsequent random numbers: %.3f\n', r1);
+

simulations/code/randomnumbers.out

@@ -0,0 +1,30 @@
+>> randomnumbers
+
+ans =
+
+   0.740875   0.193576   0.064584
+
+ans =
+
+   0.061028
+   0.695705
+   0.177097
+
+ans =
+
+   0.707430   0.404868   0.550246   0.393093
+   0.087565   0.473358   0.247850   0.161137
+
+ans =
+
+   0.350969   0.340726   0.145924   0.769714   0.203317   0.066427   0.451685   0.959766   0.850558   0.642769
+
+ans =
+
+   0.145262   0.175168   0.462693   0.089379   0.706870   0.353830   0.604305   0.405531   0.804180   0.253496
+
+ans =
+
+   0.647119   0.468534   0.484289   0.586001   0.851326   0.972554   0.014812   0.906628   0.982962   0.575003
+
+correlation between subsequent random numbers: 0.003