I am working through a statistics course right now and struggling a lot with this question. I'm not really sure where to begin.
Any reading or idea where I should begin? I really need to understand this and I just dont.
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$\begingroup$ This is often known as a variance-stabilizing transformation. The link goes to a search that points to dozens of worked examples. When "Poisson" is also included as a search term, the top hit is at stats.stackexchange.com/questions/192377. Also including "delta" produces this nice answer. $\endgroup$– whuber ♦Commented Feb 10, 2021 at 23:30
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The square root transform is the so called "variance stabilizing" transform of a Poisson distributed random variable.
The Delta Method states:
So you can easily derive the square-root function of the parameter, square it, and multiply the result by the known variance of a Poisson distributed random variable to obtain a constant variance.