SS2012-StatisticalMethods.git

@@ -0,0 +1,17 @@

+Michael Klauser Exercise 7.1

+

+We suppose 7 blue and pink balls, each of them uniquely so that we can distinguish them. 

+We only need to calculate how often we get k successes in n trials

+We can now draw n! samples of balls.

+This sample can contain the same balls but different ordered.

+Because, we have n choices for the first n-1 for the second and so on.

+General  n!

+

+but now we only want to distinguish between blue and pink balls

+for k blue balls, we again have k! possibilities to bring them in order

+similarly, for the remaining n-k balls. So we have (n-k)! possibilities.

+Now we only count the number of blue and pink balls. (we don't care about the order)

+

+ 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:

+

+ binomial coefficient = n! / (k! (n-k)!)

@@ -195,7 +195,7 @@ err_lin_m = err_lin_m[1]

-# The integration via fit is computationally expensive compared to the simple numerical integration 

+# The integration via fit (spinefun) is computationally expensive compared to the simple numerical integration by summing up. 

 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)

 text(0,2.1,strlin)

 text(0,1.6,strcon)

-#Plot errorbars quad

+#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.

 for( x in (x_vec_2)){

 tmperrup = quarel(x,best_a_qua,best_m_qua,best_b_qua) + (err_qua_a*x**2+x*err_qua_m+err_qua_b)