I am working on Kaggle Neural data challenge.
A number of spikes given a stimulus are Poisson distributed as
$$Y_i \sim P(\lambda_i)$$
The mean and variance of any Poisson process is given as
$$E[P(\lambda_i)] = Var[P(\lambda_i)] = \lambda_i$$
In order to normalize the data, the square root transformation is applied on mean and variance as,
$$E[\sqrt{P(\lambda)}] \approx \sqrt{\lambda}$$
$$Var[\sqrt{P(\lambda)}] \approx \frac{1}{4}$$
I do not understand how the variance becomes constant by square root transformation?
Update: Received an answer at Statistics