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show that standardized poisson follows poisson with mean 0 and variance 1

show that standardized poisson follows poisson with mean 0 and variance 1

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Expert Solution

Let X have a Poisson distribution with parameter λ.

Then it can be shown that the random variable

Y = (X - n)/√(n)

where n is the parameter of the Poisson distribution.

will converge to a standard normal distribution as λ goes to infinity. which is nothing but standard Normal Distribution with Mean 0 and Variance 1.

which is the Moment Generating Function of Standard Normal Distribution with mean zero and variance 1.

milcah answered 2 months ago
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