Simulating the Absent-Minded Passenger Problem with, 300, passengers, the first,

    4, of whom are absent-minded, 10000, times

                           Versus the exact results



                              By Shalosh B. Ekhad



                         The Theoretical historgram is




   +    H                                                                      
   +    HH                                                                     
0.1+    HH                                                                     
   +    HH                                                                     
   +    HH                                                                     
0.08    HH                                                                     
   +    HH                                                                     
   +    HH                                                                     
   +   H H                                                                     
0.06   H H                                                                     
   +   H H                                                                     
   +   H H                                                                     
   +   H  H                                                                    
0.04   H  H                                                                    
   +   H  H                                                                    
   +   H  H                                                                    
0.02   H  H                                                                    
   +   H  H                                                                    
   +   H  H                                                                    
   +  H    H                                                                   
  -****-+--******************************************************************- 
              50          100         150          200         250         300 


                          The simulated historgram is




   +    H                                                                      
   +    H                                                                      
3.5+    HH                                                                     
   +    HH                                                                     
  3+    HH                                                                     
   +    HH                                                                     
   +    HH                                                                     
2.5+    HH                                                                     
   +    HH                                                                     
  2+    HH                                                                     
   +   H H                                                                     
   +   H H                                                                     
1.5+   H  H                                                                    
   +   H  H                                                                    
   +   H  H                                                                    
  1+   H  H                                                                    
   +   H  H                                                                    
0.5+   H  H                                                                    
   +   H  H                                                                    
   +  H    H                                                                   
  -****-+--******************************************************************- 
              50          100         150          200         250         300 


      The true average, variance, and the scaled moments up to the 6-th are



[20.78398885, 13.41493759, 0.1816609569, 3.041562807, 1.813845275, 15.95308764]


      The simulated average, variance, and the scaled moments up to the 6-th are




[20.79300000, 13.43775100, 0.1498779946, 3.027483571, 1.417469180, 15.18808016]