original link: http://www.maths.cam.ac.uk/teaching/pastpapers/2001/Part_IA/PaperIA_2.pdf" [Broken] Question 11F Dipkomsky, a desperado in the wild West, is surrounded by an enemy gang and fighting tooth and nail for his survival. He has m guns, m > 1, pointing in different directions and tries to use them in succession to give an impression that there are several defenders. When he turns to a subsequent gun and discovers that the gun is loaded he fires it with probability 1/2 and moves to the next one. Otherwise, i.e. when the gun is unloaded, he loads it with probability 3/4 or simply moves to the next gun with complementary probability 1/4. If he decides to load the gun he then fires it or not with probability 1/2 and after that moves to the next gun anyway. Initially, each gun had been loaded independently with probability p. Show that if after each move this distribution is preserved, then p = 3/7. Calculate the expected value EN and variance Var N of the number N of loaded guns under this distribution. Hint: it may be helpful to represent N as a sum Xj (1 to m) of random variables taking values 0 and 1. This question is extremely confusing and I dunno even how to start, could anyone help?