How do I evaluate this Poisson distribution?

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Homework Help Overview

The discussion revolves around evaluating a Poisson distribution, specifically focusing on the calculation involving the parameters λ (lambda) and x. The original poster has identified their values but is uncertain about how to compute the factorial and the exponential components in the formula.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the meaning of factorial notation and provide suggestions for calculating 18!. There are questions about the use of calculators and the correct interpretation of the exponential term e^-20.

Discussion Status

Participants are actively sharing insights about the factorial function and calculator usage. Some guidance has been offered regarding where to find the factorial button on calculators, and there is acknowledgment of potential errors in calculations. The original poster expresses confusion about their results, indicating a productive exploration of the problem.

Contextual Notes

There is mention of a specific calculator model and its functions, as well as a reference to a worked answer provided in an external link. The original poster's confidence in their values for λ and x is noted, despite their ongoing struggles with the calculations.

KAISER91
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Homework Statement



How do I evaluate this Poisson distribution?

Homework Equations





The Attempt at a Solution



So I have figured out what the values for lambda and x are, but I don't know how to evaluate once I plug the values into the formula.


λ = 20
x = 18

= [ e^-20 x 20^18 ] / 18!


exp -20 x 20^18 is easy to find but how do plug in 18 factorial in the calculator?
 
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Simple do 18.17.16.15.14.13.12.11.10.9.8.7.6.5.4.3.2
 
micromass said:
Simple do 18.17.16.15.14.13.12.11.10.9.8.7.6.5.4.3.2

I'm not sure what you mean.



The answer to the question is 0.0844
 
What does 18! mean?
 
micromass said:
What does 18! mean?


I think it simply means the factorial of 18

It's from the Poisson probability distribution formula, which is;



f (x) = (e^-lambda x lambda^x ) / x!


And I just plugged in the values of x and lambda


I'm not sure how to evaluate this
 
Well, there is usually a factorial button in your calculator, somewhere.

Try under the MATH menu.
 
What does the factorial of 18 mean?

It just means 18!=18.17.16.15.14.13.12.11.10.9.8.7.6.5.4.3.2.1

Calculate it like that...
 
Char. Limit said:
Well, there is usually a factorial button in your calculator, somewhere.

Try under the MATH menu.
I have tried that several times but keep coming up with the wrong answer.

LOLI think it may be something else I'm doing wrong.e^-20 simply means the exponential of -20 ? right??
 
Char. Limit said:
Well, there is usually a factorial button in your calculator, somewhere.

Try under the MATH menu.
Yep, I see the factorial button.

I'm using a CASIO 100 so it's simply shift + x^-1 on the calculator.
 
  • #10
Well, your formula should be correct. Are you sure your x and \lambda values are correct?
 
  • #11
Char. Limit said:
Well, your formula should be correct. Are you sure your x and \lambda values are correct?
Yes I'm sure.

Let me take a screenshot of it for you.
 
  • #13
Well, I get the same answer as the book, so your calculations must be wrong somewhere.
 
  • #14
Yep.

Nevermind, I have found out my problem.

I was using the wrong button on the calculator for exponential.

LOL
 

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