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(Solved): For a given path on the grid with each step going North-East or South-East, a "peak" is any point w ...
For a given path on the grid with each step going North-East or South-East, a "peak" is any point where the path looks like
^(^())^(). So in the following path, there are 4 peaks. Consider the uniform distribution over all paths on the grid from
(0,0)to
(15,5)which only go North- East or South-East. Find the expected number of peaks. You can do this theoretically or using MCMC. If you use MCMC, state how many simulations you did and give your code. In either case, please explain your approach.
