how do u implement statistical average for a sinusoid
e.g
i want to implement process

y=(1/sqrt(N))*sum(cos(wd*cos(alphan')*t+phin'*ones(1,Ns)));

where alphan is 1 by N random mumber 
Ns=5000;
t=[0:Ns-1]*Ts
Ts= sampling period.
phin is again random number 1 by N

after summation i get y as 1 by Ns RV which is as expected. Bu tthis
is just a one sample. its mean is 0 and variance turns out to be
nearly 0.5

but due to  random nature, we should have ensemble avg 

loop=10
for i=1:loop
y(i,:)=(1/sqrt(N))*sum(cos(wd*cos(alphan')*t+phin'*ones(1,Ns)));
end

ymean=mean(y)

i believe this is how ensemble calculated

but why does variance change... should it change and if yes how to get
variance 0.5 as a single sample...

help