I have been going through Neural Networks and Deep Learning. There is a way to represent the activation of network as:
z = summation of(w*x) + b
where w,b are weight and bias with mean of 0 and S.D of 1.
where summation extends over 1 to 1000 which is total number of inputs or x. Half of them are 0 and other half is 1.
The question is to find the standard deviation of z which is given to be square root of 3/2
This question is given in the exercise. Since my stats is weak, I have been stuck in this problem and I cannot figure out how to get the value. I considered that since W and X are independent, the variance of Z is Var(W) * Var(X). But Var(X) = 250 and its far off from the given answer.
I would be thankful if someone can help me.
P.S: If somebody wants to know more information than please open the link and Ctrl-F for "Verify that the standard deviation". This will highlight the question there.