SOCR EduMaterials Activities Discrete Distributions

This is an activity to explore the Poisson Probability Distribution.

• Description: You can access the applets for the above distributions at http://www.socr.ucla.edu/htmls/SOCR_Distributions.html .

• Exercise 1: Use SOCR to graph and print the distribution of a Poisson random variable with \( \lambda=2 \). What is the shape of this distribution?

• Exercise 2: Use SOCR to graph and print the distribution of a Poisson random variable with \( \lambda=15 \). What is the shape of this distribution? What happens when you keep increasing \( \lambda \)?

• Exercise 3: Let \( X \sim Poisson(5) \). Find \( P(3 \le X < 10) \), and \( P(X >10 | X \ge 4) \).

• Exercise 4: Poisson approximation to binomial: Graph and print \( X \sim b(60, 0.02) \). Approximate this probability distribution using Poisson. Choose three values of \( X \) and compute the probability for each one using Poisson and then using binomial. How good is the approximation?

Below you can see the distribution of a Poisson random variable with \( \lambda=5 \). In this graph you can also see the probability that between 2 and 5 events will occur.

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• SOCR Home page: http://www.socr.ucla.edu

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