Show under what condition Poisson distribution tends to Normal distribution.
The Poisson distribution is defined as: [ P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!}, \quad k = 0, 1, 2, \dots ] where (\lambda) is the mean and variance of the distribution. The mean and variance are equal: [ \mu = \sigma^2 = \lambda ] To see when the Poisson distribution approaches the Normal distribution, consider the limit of large (\lambda). For large (\lambda), (k!) can ____ ________ __________ ______ __________ _____ ________ ___ ______ ________ ___ _________.
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A proton inside a nucleus
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