Question $4$: Bounded Random Walk

In a bounded rankom walk, a ball starts its journey from the widdle ovtl. It can move is

four diesction $($up$,$ down, right, left$)$ with squal probabalities within a bounded arta. Sisce it

is a bousded awa, the ball casnot mowe in all four directions if certain cases. Foe example.

when the bottom boundary as Point $B($excluting the comers$)$ is roarbod, the nest step call

go left, up$,$ if right ouly as cas be: swen from the figure below $($again with squal probabilitiss$).$

Similarly, wben a comes is racherd as Point $C,$ the next stegs can be in two directions only.

Figure $1$ illustrates the random walk in a grid see of $5x5.$

Figure a: Inatration of the perblitm

To simalate bousdod randow walk problem, write a MNTLAB script that tales these: inputs

from the toer ulich afe,

grid size $N,$

a specific target cell within the bousded area, $($its $x$ and y coodinates are prowided

separately$)$

a spocific number of stepo, $t($for plotting purposes$)$

Part I: Your script should output

number of steps ropuirod for the first passage: from the specific cell giwte by the wore,

A figure that shous $x-$coocimates of the trajectory for the muber of stepe $(t)$ dotermind

by the user

A figure that shows y$-$coodimates of the trajectary for the muber of steps $(t)$ dotermind

by the user.

Pleace note that initial location of the ball is the ovater of the grid $($its coordisate is

costimue untal the: specific ofll detwanined by the user is reached.

Be careful that the specific step number that is taben as user input may be greater

than the total number of stegs the ball has tabue. In such a case, you nosd to plat $x-$

coocdinate trajectory asd y$-$coordinate trajectory until the total number of steps taben.

not the spreific step number.