The number of quote updates in a minute is Poisson with mean 6. What is the ratio P(X = 5) / P(X = 3), where X is the number of updates?

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Poisson count ratio

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The number of quote updates in a minute is Poisson with mean $6$ . What is the ratio $\frac{P ( X = 5 )}{P ( X = 3 )}$ , where $X$ is the number of updates?

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Hint

The common factors cancel in the ratio of Poisson probabilities.

Solution

The probability is $P (X = k) = e^{- 6} \frac{6 ^{k}}{k !}$ .
In the ratio, $e^{- 6}$ cancels and what remains is $\frac{6 ^{2}}{5 \times 4}$ .
This equals $\frac{36}{20}$ , which reduces to $\frac{9}{5}$ .

Answer: $\frac{9}{5}$

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