This is a matlab code that could generate a random walk in two dimensions of length 1000: xy = cumsum (-1+2*rand(1000,2),1).
The 'stepsize' is between $[-1,1]$. In this case, we are talking about the set of real numbers from $-1$ and $1$. The rand function in this case generates numbers between $(0,1)$ over a uniform distribution.
Question 1: How will I determine the range of values (in $x$ and $y$ coordinates) after covering 1000 steps?
Question 2: Is it possible to find the values of $a$, $b$, with at least a probability of 0.5, so that $a + bU(0,1)$ gives me a random walk where the extreme points are in the domain $X: [860,1520]$ and $Y:[-830,0]$? after 600 steps?
$U(0,1)$ means the uniform distribution over $(0,1)$.
Your insights would be very helpful.