# SOCR EduMaterials Activities Poisson Distribution

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## This is an activity to explore the Poisson Probability Distribution.

• Exercise 1: Use SOCR to graph and print the distribution of a Poisson random variable with λ = 2. What is the shape of this distribution?
• Exercise 2: Use SOCR to graph and print the distribution of a Poisson random variable with λ = 15. What is the shape of this distribution? What happens when you keep increasing λ?
• 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 λ = 5. In this graph you can also see the probability that between 2 and 5 events will occur.