Did I set the problem correctly?

https://gyazo.com/a6c00ee08cdd03c313b4be970d361ac0

This is my code:

clear all;clc;

N=1;

SI= exp(-1.*N);

tol = 10.^(-1.*10);

y = zeros(1,0);

while 1,

   SI= exp(-1.*N);

y(1,end+1) = SI + rand;

    if SI<=tol

        break;

    end

    N=N+1;

end

k=0:10:230;

y

N ;%number of iterations N that were required for convergence

%Plotting

plot(k,y)