Statistics MCQs, Data Analysis, Stat Software
Stochastic Processes, Markov Process, Random Walk Models, Poisson Process, Brownian Process, Random Walk Probability
A Markov chain, named after Andrey Markov is a mathematical system that experiences transitions from one state to another, between a finite or countable number of possible states. Markov chain is a random process usually characterized as memoryless: the next state depends only on the current state and not on …
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 positive steps (+1) and $L_n$ …
A simple random walk (or unrestricted random walk) on a line or in one dimension occurs with probability $p$ when the walker steps forward (+1) and/or has probability $q=1-p$ if the walker steps back ($-1$). For ith step, the modified Bernoulli random variable $W_i$ (takes the value $+1$ or $-1$ …
A random walk (first introduced by Karl Pearson in 1905) is a mathematical formalization of a path consisting of a series of random steps. Random Walks Example The following are some example related to random walks Suppose there are $a+1$ positions marked out on a straight line and numbered 0,1,2,…, …