Calculating Probability using the Poisson Distribution

Thread starter sol59
Start date Dec 11, 2016
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Distribution Poisson Poisson distribution Probability Probability distribution

In summary: P(Y=1)=((2*1/6)1*(e-1/3))/1!=0.4779:00-9:10 P(Y=0)=((2*1/6)0*(e-1/3))/0!=0.7169:10-9:50 1 student...P(Y=1)=((2*1/6)1*(e-1/3))/1!=0.477In summary, the probability of having 0 students arrive between 9 and 9:10 is 0.716, and the probability of having 1 student arrive between 9:10 and 9:50 is 0.477. To find the probability

Dec 11, 2016

sol59

haruspex said:

You got there!

Thank you so much for your help! I've managed to solve all other problems but this one was too difficult for me:) Thanks again:)!

<h2>What is the Poisson Distribution?</h2><p>The Poisson Distribution is a statistical distribution that is used to model the probability of a certain number of events occurring within a fixed interval of time or space. It is often used to analyze rare events or events that occur randomly.</p><h2>What are the assumptions of the Poisson Distribution?</h2><p>The Poisson Distribution assumes that the events occur independently of each other, the average rate of events is constant, and the probability of an event occurring in a small interval of time or space is proportional to the size of the interval.</p><h2>How is the Poisson Distribution different from the Normal Distribution?</h2><p>The Poisson Distribution is different from the Normal Distribution in that it is used to model discrete events, while the Normal Distribution is used to model continuous events. Additionally, the Poisson Distribution has only one parameter (the average rate of events), while the Normal Distribution has two parameters (mean and standard deviation).</p><h2>When should the Poisson Distribution be used?</h2><p>The Poisson Distribution should be used when analyzing rare events or events that occur randomly, such as the number of accidents in a day or the number of customers arriving at a store in an hour. It is also used in situations where the number of events is limited to a specific time or space interval.</p><h2>How is the Poisson Distribution calculated?</h2><p>The Poisson Distribution is calculated using the formula P(x) = (e^-λ * λ^x) / x!, where λ is the average rate of events and x is the number of events. This formula can be used to calculate the probability of a specific number of events occurring within a fixed interval of time or space.</p>

FAQ: Calculating Probability using the Poisson Distribution

What is the Poisson Distribution?

The Poisson Distribution is a statistical distribution that is used to model the probability of a certain number of events occurring within a fixed interval of time or space. It is often used to analyze rare events or events that occur randomly.

What are the assumptions of the Poisson Distribution?

The Poisson Distribution assumes that the events occur independently of each other, the average rate of events is constant, and the probability of an event occurring in a small interval of time or space is proportional to the size of the interval.

How is the Poisson Distribution different from the Normal Distribution?

The Poisson Distribution is different from the Normal Distribution in that it is used to model discrete events, while the Normal Distribution is used to model continuous events. Additionally, the Poisson Distribution has only one parameter (the average rate of events), while the Normal Distribution has two parameters (mean and standard deviation).

When should the Poisson Distribution be used?

The Poisson Distribution should be used when analyzing rare events or events that occur randomly, such as the number of accidents in a day or the number of customers arriving at a store in an hour. It is also used in situations where the number of events is limited to a specific time or space interval.

How is the Poisson Distribution calculated?

The Poisson Distribution is calculated using the formula P(x) = (e^-λ * λ^x) / x!, where λ is the average rate of events and x is the number of events. This formula can be used to calculate the probability of a specific number of events occurring within a fixed interval of time or space.