A group of researchers on average observe 5 bacteria in a specific area of a slide containing a sample of well water. What could be the distribution of the number of bacteria? ii. Determine P(X > 2). Bonus [1pt]: Let X be a Poisson random variable with a parameter. Determine the probability that X is even. Hint: Use Taylor's formula, e^(-λ) + e^(-λ)λ^2/2.
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The parameter of the Poisson distribution is λ = 5, since on average we observe 5 bacteria. ii) To determine P(X > 2), we can use the Poisson probability mass function: P(X > 2) = 1 - P(X ≤ 2) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)] Using the Poisson probability Show more…
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