Problem 4: Panzer Problem [25% points] Military engineers from Allied Forces in World War II found out that a factory in Nazi Germany manufactures the Panzers (German tanks) enumerated consequently from 1 to N. Although the number N is unknown, there is a certain intelligence that it can not be more than 20 but any other value is equally likely. 1 It can be shown to be convergent in a system called 2-adic numbers 3a) Calculate every probability, pi , that the factory produced xi = N panzers in total given the serial number of the captured panzer happened to be 12. Notes: Express your results in a table. Show how you did the calculations (at least for one case). You may use Excel or a similar tool explaining how you used it. Hints: You can use Bayes' Rule. You may assign event A as the serial number of captured Panzer is 12, and events Bi as the maximum serial number of produced Panzers is xi = N. b) Verify that the total probabiliy is 1. c) Plot a graph of xi v. pi from this table. If you plot it by hand please use a grid paper. You may use Excel or similar tools (recommended). d) Calculate the mean, x, and the variance, s 2 , from this distribution where they are dened in terms of probabilities, respectively as: x = Xpixi s 2 = Xpi(xi x