add 7.1 and finished 7.2
Michi

Michi commited on 2012-06-11 19:37:32
Zeige 2 geänderte Dateien mit 19 Einfügungen und 2 Löschungen.

... ...
@@ -0,0 +1,17 @@
1
+Michael Klauser Exercise 7.1
2
+
3
+We suppose 7 blue and pink balls, each of them uniquely so that we can distinguish them. 
4
+We only need to calculate how often we get k successes in n trials
5
+We can now draw n! samples of balls.
6
+This sample can contain the same balls but different ordered.
7
+Because, we have n choices for the first n-1 for the second and so on.
8
+General  n!
9
+
10
+but now we only want to distinguish between blue and pink balls
11
+for k blue balls, we again have k! possibilities to bring them in order
12
+similarly, for the remaining n-k balls. So we have (n-k)! possibilities.
13
+Now we only count the number of blue and pink balls. (we don't care about the order)
14
+
15
+ Now we can divide the overall-number of possibilities n! by the number of possibilities for the blue balls k! and by the number of possibilities for pink  balls (n-k)!. We remember that  all events are statistically independent, this yields:
16
+
17
+ binomial coefficient = n! / (k! (n-k)!)
... ...
@@ -195,7 +195,7 @@ err_lin_m = err_lin_m[1]
195 195
 
196 196
 
197 197
 
198
-# The integration via fit is computationally expensive compared to the simple numerical integration 
198
+# The integration via fit (spinefun) is computationally expensive compared to the simple numerical integration by summing up. 
199 199
 
200 200
 
201 201
 strqua = paste("quadratic: ax^2 + mx +b with a=",round(best_a_qua,2),"+-",round(err_qua_a,2),",\n m=", round(best_m_qua,2),"+-",round(err_qua_m,2),", b=",round(best_b_qua,2),"+-",round(err_qua_b,2))
... ...
@@ -206,7 +206,7 @@ text(0,2.8,strqua)
206 206
 text(0,2.1,strlin)
207 207
 text(0,1.6,strcon)
208 208
 
209
-#Plot errorbars quad
209
+#Plot errorbars quad. Here i'm not sure how to plot the error bars so I plot them like done below. An explanation about how to plot error bar in the tutorial would be nice.
210 210
 for( x in (x_vec_2)){
211 211
 
212 212
 tmperrup = quarel(x,best_a_qua,best_m_qua,best_b_qua) + (err_qua_a*x**2+x*err_qua_m+err_qua_b)
213 213