Basic Statistics20815 marksNumerical: Poisson distribution probabilityPoisson distribution
A server records the number of requests per minute, which follows a Poisson distribution with a mean of 5 requests per minute. (a) What is the probability that exactly 3 requests occur in a given minute? (b) What is the probability that more than 2 requests will occur? λ=5\lambda = 5λ=5
A server records the number of requests per minute, which follows a Poisson distribution with a mean of 5 requests per minute. (a) What is the probability that exactly 3 requests occur in a given minute? (b) What is the probability that more than 2 requests will occur? λ=5\lambda = 5λ=5[5]
- Distribution: Poisson - Mean rate: $\lambda = 5$ requests per minute - Interval: 1 minute - (a) Find $P(X = 3)$ - (b) Find $P(X 2)$ Poisson formula: $$P(X = k) = \frac{e^{-\lambda}\lambda^k}{k!}, \quad \lambda = 5$$ Note: $e^{-5} \approx 0.0067379$ --- $$P(X = 3) = \frac{e^{-5}\cdot 5^3}{3!} = ...