In a three$-$dimensional random walk, the position $($x$,$ y$,$ z$)$ of a walker at step j is computed

by: xj $=$ xj$-1+\backslash$Delta x$,$ yj $=$ yj$-1+\backslash$Delta y and zj $=$ zj$-1+\backslash$Delta z$,$ where $\backslash$Delta x$,\backslash$Delta y$,$ and $\backslash$Delta z are random numbers

that determine the length and direction of each step. Assume that the walker starts at the

origin, and keeps taking steps $($each of random length and direction$)$ until they step outside of

a boundary. The boundary is a sphere of radius R $=15$ centered at the origin.

a$.$ Write a Matlab script $($m$-$file$)$ that calculates the number of steps required for the walker

to reach the boundary. Use Matlab$$s built$-$in function randn$(1,1)$ to calculate $\backslash$Delta x$,\backslash$Delta y$,$ and

$\backslash$Delta z$.$ Run the program $500$ times $($using a loop$)$ and calculate the average number of steps

needed to reach the boundary. Output the results to the user.

b$.$ Write a Matlab script $($m$-$file$)$ that creates a three$-$dimensional plot of a single random

walk. Use Matlab$$s built$-$in function randn$(1,1)$ to calculate $\backslash$Delta x$,\backslash$Delta y$,$ and $\backslash$Delta z$.$ Use

Matlab$$s built$-$in function plot$3$ to create the plot. Be sure to add a title and axis labels to

the plot.