central limit theorem random process

ho i need to generate the next equsion x[n]=sigma(w[n]) where w[n] gets probability of 1 and -1 ,and to check the charachteristic, for N LARGE enough to see the variance and the mu..well i stuck at the beginnig can genrate a vector of 1 and -1

for i=1:N
x(1,:)=(-1)^i*(rand(1,1000))
if x(1,i)<=0
x(1,i)=-1
else 
x(1,i)==1 
end 

its get the correct vector.. any body help

Answer 1

[John D'Errico]

What would this do?

rand(1,N)

So then, what would this do, if I appended a round on top? I.e.,

round(rand(1,N))

What possible values could result from that? Would the possible results be equally probable? But, now what if I multuplied by 2?

round(rand(1,N))*2

Now what values can you get? Does it seem we are getting close? So what if we subtracted 1?

round(rand(1,N))*2 - 1