Probability using Poisson Distribution

In summary, the conversation discusses using Poisson's distribution to calculate the probability of typographical errors in a book of 600 pages. The equation W(n) = \lambdan e -\lambda / n! is used, with lambda representing the mean number of errors per page. The goal is to find the probability of a page containing no errors (0.37) and at least three errors. One participant suggests that lambda should be 1, which leads to a probability of 0.37 for a page containing no errors.
  • #1
FourierX
73
0

Homework Statement



Suppose a typographical errors committed by a typesetter occurs randomly. If that a book of 600 pages contains 600 such errors, calculate the probability by using Poisson's distribution.
i) that a page contains no errors
ii) that a page contains at least three errors


Homework Equations



W(n) = [tex]\lambda[/tex]n e -[tex]\lambda[/tex] / n!

The Attempt at a Solution



I related [tex]\lambda[/tex] = Np, the mean number of errors and proceeded. I am supposed to get 0.37 for part i) of the problem but I didn't get it right. Any suggestion?


Berkeley
 
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  • #2
Isn't lambda the mean number of errors per page? If so, it would be 1. Using the formula, W(0) = 1^0 * e^(-1)/0! = 1/e ~ .37
 

Related to Probability using Poisson Distribution

What is Poisson Distribution?

Poisson Distribution is a mathematical concept used to model the probability of a certain number of events occurring within a specific time period, space, or volume, when the events occur independently and at a constant rate. It is often used to predict rare events or random occurrences, such as the number of customers arriving at a store in a given hour or the number of car accidents in a day.

What is the formula for calculating Poisson Distribution?

The formula for Poisson Distribution is P(x) = (e^(-λ) * λ^x) / x!, where P(x) is the probability of x events occurring, e is the base of natural logarithm, λ is the average rate of event occurrence, and x is the number of events.

What is the difference between Poisson Distribution and Normal Distribution?

The main difference between Poisson Distribution and Normal Distribution is that Poisson Distribution is used to model the probability of rare events, while Normal Distribution is used for continuous data and assumes a bell-shaped curve. Poisson Distribution is based on discrete data and assumes a skewed distribution.

What are the assumptions of Poisson Distribution?

The assumptions of Poisson Distribution include: (1) the events occur independently of each other, (2) the average rate of event occurrence remains constant over time, (3) the probability of an event occurring in a short time interval is proportional to the length of the interval, and (4) the probability of more than one event occurring in a short time interval is negligible.

How can Poisson Distribution be used in real life?

Poisson Distribution can be used in various real-life scenarios, such as predicting the number of phone calls a call center will receive in a day, estimating the number of accidents on a highway in a month, or calculating the number of defects in a batch of products. It is also commonly used in sports analytics to predict the number of goals or points a team will score in a game.

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