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Problem 2 Alice is a goaltender in an ice hockey team. Suppose that the number of goals she concedes each game is distributed as a Poisson distribution with parameter A = 5. (Recall that if X~ Poisson (A), then P(X = n)= " for each n ≥ 0.) Assume that the number of the goals she concedes at different games are independent of each other. Alice gets a medal after each game if and only if she concedes zero or one goal in that game. What is the distribution of the number of games she plays to get her first (b) medal? What is the expected number of games she plays to get her third medal? (c) What is the probability that she will receive strictly more than two medals in the first 30 games?

Problem 2 Alice is a goaltender in an ice hockey team. Suppose that the number of goals she concedes each game is distributed as a Poisson distribution with parameter A = 5. (Recall that if X~ Poisson (A), then P(X = n)= " for each n ≥ 0.) Assume that the number of the goals she concedes at different games are independent of each other. Alice gets a medal after each game if and only if she concedes zero or one goal in that game. What is the distribution of the number of games she plays to get her first (b) medal? What is the expected number of games she plays to get her third medal? (c) What is the probability that she will receive strictly more than two medals in the first 30 games?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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## Problem 2 Alice is a goaltender in an ice hockey team. Suppose that the number of goals she concedes each game is distributed as a Poisson distribution with parameter λ = 5. (Recall that if \( X \sim \text{Poisson}(\lambda) \), then \( P(X = n) = \frac{e^{-\lambda} \lambda^n}{n!} \) for each \( n \geq 0 \).) Assume that the number of goals she concedes at different games are independent of each other. Alice gets a medal after each game if and only if she concedes zero or one goal in that game. (a) **What is the distribution of the number of games she plays to get her first medal?** (b) **What is the expected number of games she plays to get her third medal?** (c) **What is the probability that she will receive strictly more than two medals in the first 30 games?**
Transcribed Image Text:## Problem 2 Alice is a goaltender in an ice hockey team. Suppose that the number of goals she concedes each game is distributed as a Poisson distribution with parameter λ = 5. (Recall that if \( X \sim \text{Poisson}(\lambda) \), then \( P(X = n) = \frac{e^{-\lambda} \lambda^n}{n!} \) for each \( n \geq 0 \).) Assume that the number of goals she concedes at different games are independent of each other. Alice gets a medal after each game if and only if she concedes zero or one goal in that game. (a) **What is the distribution of the number of games she plays to get her first medal?** (b) **What is the expected number of games she plays to get her third medal?** (c) **What is the probability that she will receive strictly more than two medals in the first 30 games?**
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