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Right, so what is the probability of at least 1 arrival in (9:10, 9:50) ?sol59 said:
Calculating Probability using the Poisson Distribution
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SUMMARY
The discussion focuses on calculating the probability of student arrivals using the Poisson distribution and the Exponential distribution. The average arrival rate is established at λ = 2 students per hour. The key challenge is determining the probability that the time between two consecutive arrivals falls within the interval of 10 to 50 minutes. The final probability calculated for the scenario is approximately 0.527, representing the likelihood of no arrivals in the first 10 minutes and at least one arrival in the subsequent 40 minutes.
PREREQUISITES- Understanding of Poisson distribution and its parameters (λ and k)
- Knowledge of Exponential distribution and its application in waiting time problems
- Familiarity with basic probability concepts and calculations
- Ability to interpret mathematical equations related to probability
- Study the derivation and applications of the Poisson distribution in real-world scenarios
- Learn how to apply the Exponential distribution to model waiting times
- Explore advanced topics in probability theory, such as conditional probability and memoryless properties
- Practice solving problems involving multiple distributions to enhance analytical skills
Students, educators, and data analysts interested in probability theory, particularly those working with arrival processes and statistical modeling in various fields such as operations research and queueing theory.
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