Binomial vs. Poisson

Binomial Distribution Poisson Distribution
Fixed Number of Trials (n)
[10 pie throws]
Infinite Number of Trials
Only 2 Possible Outcomes
[hit or miss]
Unlimited Number of Outcomes Possible
Probability of Success is Constant (p)
[0.4 success rate]
Mean of the Distribution is the Same for All Intervals (mu)
Each Trial is Independent
[throw 1 has no effect on throw 2]
Number of Occurrences in Any Given Interval Independent of Others
Predicts Number of Successes within a Set Number of Trials Predicts Number of Occurrences per Unit Time, Space, ...
Can be Used to Test for Independence Can be Used to Test for Independence