Question

The distribution function W(x) for a one dimensional random walk gives the probability that an object moving randomly in the +x and -x directions is displaced by a distance x after N jumps, each jump of length l. The displacements are normally distributed which means the distribution function is W(x)=(1/sqrt2πσ^2)e^(−(x−<x>)^2)/2σ^2). In the displacement function, <x> is the average displacement <x>=Nl(p−q) and the variance is σ^2=<x^2>−<x>^2=4pqNl2σ^2. The parameter p is the probability of a displacement in the +x direction and q is the probability of a displacement in the -x direction. The variance σ^2 is a measure of the dispersion of the displacements.

The square root of the variance is the standard deviation σ. What is the probability that after N=20 jumps the organism will be found between x=0.00mm and x=0.224mm? Give your answer as a number between 0 and 1?

Answer 1