Statistics I20765 marksNumerical: Poisson distribution probabilityDiscrete distributions
Message arrives at an electronic message center at random times, with an average of 9 messages per hour. a. What is the probability of receiving at least four messages during the next hour? b. What is the probability of receiving at most three messages during the next hour?
Message arrives at an electronic message center at random times, with an average of 9 messages per hour. a. What is the probability of receiving at least four messages during the next hour? b. What is the probability of receiving at most three messages during the next hour? [5]
- Average rate: 9 messages per hour - Time interval: next 1 hour - Model: Poisson distribution - Parameter: $\lambda = 9$ Poisson probability mass function: $$P(X = x) = \frac{e^{-\lambda}\lambda^x}{x!}, \quad \lambda = 9$$ With $e^{-9} = 0.00012341$. Using the complement: $$P(X \geq 4) = 1 - [P(...