How do I evaluate this Poisson distribution?

In summary, the homework statement is to evaluate a Poisson distribution. The Attempt at a Solution tells the reader how to find the value of lambda and x, but the reader is still unsure of how to evaluate the equation. The final summary indicates that the problem lies with the use of the wrong button on the calculator, and that the reader has found the problem.
  • #1
KAISER91
27
0

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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  • #2
Simple do 18.17.16.15.14.13.12.11.10.9.8.7.6.5.4.3.2
 
  • #3
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
 
  • #4
What does 18! mean?
 
  • #5
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
 
  • #6
Well, there is usually a factorial button in your calculator, somewhere.

Try under the MATH menu.
 
  • #7
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...
 
  • #8
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??
 
  • #9
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 [itex]\lambda[/itex] values are correct?
 
  • #11
Char. Limit said:
Well, your formula should be correct. Are you sure your x and [itex]\lambda[/itex] 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
 

Related to How do I evaluate this Poisson distribution?

1. What is a Poisson distribution and how is it used in science?

A Poisson distribution is a probability distribution that models the number of events occurring within a specific time or space when the events are independent and the average rate of occurrence is known. It is commonly used in science to analyze and predict rare events, such as the number of mutations in DNA or the number of radioactive particles emitted from a substance.

2. How do I calculate the mean and variance of a Poisson distribution?

The mean and variance of a Poisson distribution can be calculated using the formula: mean = rate parameter and variance = mean. For example, if the average rate of occurrence is 5, then the mean and variance would both be 5.

3. Can a Poisson distribution be used for continuous data?

No, a Poisson distribution is only suitable for discrete data, meaning that the data can only take on whole number values.

4. How do I determine if a dataset follows a Poisson distribution?

To determine if a dataset follows a Poisson distribution, you can plot the data on a histogram and see if it resembles the typical shape of a Poisson distribution, which is a skewed right, bell-shaped curve. You can also use statistical tests, such as the chi-square test, to assess the goodness of fit to a Poisson distribution.

5. What are the limitations of using a Poisson distribution?

A Poisson distribution assumes that the events are independent and occur at a constant rate, which may not always be the case in real-world situations. It also only works for discrete data and may not be suitable for datasets with large values or a wide range of values. Additionally, the accuracy of predictions using a Poisson distribution decreases as the mean increases.

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