- 1 Consider The Classical Random Walker Moving On The Line One Step To The Right Or To The Left With Probabilities P An 1 (98.67 KiB) Viewed 24 times
least part 1 if possible
1. Consider the classical random walker, moving on the line one step to the right or to the left with probabilities p and q, respectively, where p, q> 0 and p+q = 1. Initially, р at time t = 0, the walker is at x = 0. We are interested in the probability p(m, N) that the walker will be at x = m at time t = N. Prove that when -N <m <N, N Nm N+m Nem 2 9 if N + m is even www-{{4 {( ਪੰਧ ) *** p(m, N) = otherwise, i.e. the binomial distribution. What is p(m, N) when m<-N or m > N? 2. Show that the average displacemeny of the walker after N steps is N (p – q). 3. Show that the variance of the distribution is o2 = 4Npq. .