The number of emergency admissions each day to a hospital is found to have Poisson’s distribution with mean 4. What is the probability that on a particular day there will be no emergency admissions?

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This question was previously asked in

ESE Electrical 2021 Official Paper

Answer 1

Let X represent the number of emergency admissions each day to a hospital.

Given X is Poisson random variable with a mean (λ) = 4

Now, P(X) = \(\frac{e^-\lambda \times \lambda^X}{X!}\) .... (1)

On a particular day there will be no emergency admissions:

Hence, X = 0

From equation (1),

P(X) = \(\frac{e^{-4}\times 4^0}{0!}=e^{-4}\)