tag:blogger.com,1999:blog-4115025577315673827.post2962890935863748419..comments2020-05-25T13:34:36.365+05:30Comments on CSE Blog - quant, math, computer science puzzles: 100 Locomotives ProblemPratik Poddarhttp://www.blogger.com/profile/11577606981573330954noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-4115025577315673827.post-78955490412158945532010-03-26T14:44:22.960+05:302010-03-26T14:44:22.960+05:30@Everyone,
This is not an exact question. This is ...@Everyone,<br />This is not an exact question. This is more of a qualitative question. I need to see various approaches to solve this problem. I see this as a real problem: I am seeing locomotives and someone asks me: "Guess the number of locomotives".<br /><br />Since I have not provided enough data, all "creative" answers are correct.Pratik Poddarhttps://www.blogger.com/profile/11577606981573330954noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-88687977436081076182010-03-25T21:24:58.014+05:302010-03-25T21:24:58.014+05:30@Tiger- The difference in our views is due to the ...@Tiger- The difference in our views is due to the way we have interpreted the question. You have treated N as a random variable and I have treated it as an unknown which we need to guess.<br /><br />In my case, the random variable is the number of the vehicle spotted on a particular day whose density I have assumed to be uniform. The only dilemma I have in my mind is that I have used Expectation measure to predict the outcome of a single trial, which in practice is ought to give erroneous results.<br />But I had no other choice.<br /><br />Conclusively, I guess the question should be more specific about what assumptions we need to make.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-2163374040773869802010-03-25T13:33:15.659+05:302010-03-25T13:33:15.659+05:30@Aman:- That makes no sense. Perhaps there's s...@Aman:- That makes no sense. Perhaps there's some part I'm missing here.<br /><br />You have to maximise P(N|100). What you have done is to solve E[x|N]=100. The two have no obvious connection. <br /><br />I doubt if you can solve this unless you have some sort of idea about the distribution of N. Clearly if it is a real company, N cannot be arbitrarily large(there's a limit to how many rail carriages can be made from the Earth's crust)<br /><br />Thus, we could probably assume a gaussian distribution for N centered around some mean with some variance and then maximise P(N|100).Tigerhttps://www.blogger.com/profile/14382175653187845546noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-36817331170004661122010-03-17T18:54:59.554+05:302010-03-17T18:54:59.554+05:30The first part is easy.Assuming each locomotive ha...The first part is easy.Assuming each locomotive has probability 1/N of being spotted, the Expected number of locomotive spotted at a point of time is (N+1)/2.Which yields N=199.<br /><br />For the 2nd part, the expected value of the maximum number seen is:<br />1/C(n,5) * ( n*C(n,4) + (n-1)*C(n-1,4) +........+ 4*C(4,4))<br /><br />Couldn't solve this for n.<br />But a general intuition says that the 5 randomly chosen numbers would in a long run be centered around equi-spaced points in the interval (1,N) i.e. around N/6, 2N/6,....5N/6 respectively.<br />So that the expected value of maximum is 5N/6 or N=120.Anonymousnoreply@blogger.com