#### add 7.1 and finished 7.2 Michi authored on 11/06/2012 19:37:32
Showing 2 changed files
 1 1 `new file mode 100644` ... ... `@@ -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` 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)`