Statistical physics $2($G$032)$ HW$1($ Sep. $2723$:$59)$

$(1)$ Simulate two$-$dimensional random walk from the origin $(0,0)$ for three different number of steps $N=10,N=100,N=1000.$ Number of iterations is $5.$ You can use any program whatever you can use. $($e$.$g$.$ python, excel, mathlab, etc.$)$

$(2)$ Find the average of $r^2$ when $N=100$ for $1000$ iterations. $r$ is distance from the origin.

$(3)$ Calculate $($:$r^2$:$)$ and compare this to the result of $(2).$