Need assistance with solving question 1 part d. Do I just substitute square root lambda as parameter in Poisson distribution and solve for MLE? Part d is as follows:

"It is often desirable for the mean and variance of a random variable to be unrelated

(e.g., normal distribution). This is clearly not true for the Poisson, but a suitable

transformation could ameliorate this problem. Suggest and justify an estimator

for the transformation h(?) =??, and determine its asymptotic distribution including the variance."

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