Week 5: Poisson probability model
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6 Terms
What is the poisson model good for?
In the binomial formula if the number of trials (n) is a really large number, it can be intractable.
The poisson model bypasses this
What are the limitations of using the poisson model?
Poisson can only be used if the expected number of successes or failures is less than 10!
if expected value of binomial is less than 10
if E[V] = n x p < 10
n = # of trials
p = probability of success
![<p>Poisson can only be used if the expected number of successes or failures is less than 10!</p><ul><li><p>if expected value of binomial is less than 10</p></li></ul><ul><li><p>if E[V] = n x p < 10</p></li></ul><p>n = # of trials</p><p>p = probability of success</p><p></p>](https://knowt-user-attachments.s3.amazonaws.com/70db6562-4a17-4653-a851-4321f3a81750.png)
What is the poisson model formula?
λ (lambda) = mean number of success (np)
n = # of trials
p = probability of success
X = number of successes
What is the expected value, variance, and standard deviation in the poisson model?
What is the poisson process? (λ as a rate)
λ is the average number of successes per unit time
→ can be converted to per hour or per minute
What are the conditions for the poisson process?
We know the average rate (λ) which is the average number of successes per unit
The probability of success is the same for each equally sized unit
What happens in one unit does not influence other units (independence)