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Homework Statement
A man wants to travel to four cities (A,B,C,D) but he has such a bad memory that he can't remember the cities that visited, therefore, if he travel to city A he can choose between (B,C,D) and if he then travel to B he can choose between (A,C,D).
Find v, If v it's the expected value of how many times he would have to travel before visited all cities at least once.
Homework Equations
X= "# of times required to visit all cities at least once."
[itex]E(X) = \Sigma xp_{X}(x)itex]
The Attempt at a Solution
I'm having some issue trying to find the probability function [itex]p_{X}(x)[/itex].
Since he already traveled to some city -let's say A- and then travels to another city -let's say B-, then P("going to another city not traveled before") = {C,D}/{A,C,D} = 2/3.
It seems to me that P{X=4}= (2/3)*(1/3).
Now, how can i get P {X=n} ?. I've been thinking about a binomial distribution, but it doesn't seem quite right because with X~Bin(n,p) i can't just use one value of p -that changes depending of how many different cities he already visited.