Write a function

$>$ MovingParticle$<-$function$()$

which returns the trajectory of particle$$s move. The positions Ak should be stored as columns of a matix with two rows.

ii$.$ Plot $4$ trajectories of the random walks generated by your code.

iii. Use a Monte Carlo simulation with at least $1000$ repeated experiments to estimate the prob$-$

ability that the MovingParticle comes back to the origin $(0,0)-$ in at most $10$ steps

$-$ in at most $100$ steps

$-$ in at most $200$ steps

iv$.$ Use a Monte Carlo simulation with at least $1000$ repeated experiments to estimate the avarage number of steps needed that the MovingParticle comes back to the origin $(0,0)$

$-$ in at most $10$ steps $-$ in at most $100$ steps $-$ in at most $200$ steps

SOLVE USING R PROGRAM