Random Walk Probability of Returning to Origin after n steps

Random Walk Probability of Returning to Origin Assume that the walk starts at $x=0$ with steps to the right or left occurring with probabilities $p$ and $q=1-p$. We can write the position $X_n$ after $n$ steps as\[X_n=R_n-L_n \tag{1}\]where $R_n$ is the number of right or …

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