Poisson Distribution
P(X = k) = (ฮปk · eโฮป) / k!
Practical Examples
๐ Call Center
Average 3 calls/hour. What is P(exactly 2 calls)?
ฮป=3, k=2
๐ญ Product Defects
Average 4.5 defects/batch. P(6 defects)?
ฮป=4.5, k=6
๐ Customer Arrivals
Average 10 customers/hour. P(8 arrive)?
ฮป=10, k=8
๐ Software Bugs
Average 2 bugs/1k lines. P(0 bugs)?
ฮป=2, k=0
โก Server Failures
Average 0.5 failures/month. P(1 failure)?
ฮป=0.5, k=1
๐ง Email Volume
Average 20 emails/day. P(15 emails)?
ฮป=20, k=15
About the Poisson Distribution
What is the Poisson Distribution?
The Poisson distribution is a discrete probability distribution that models the number of events occurring in a fixed interval of time or space, given a known constant mean rate.
Conditions for Use:
โข Events occur independently of each other
โข The average rate ฮป is constant over the interval
โข At most one event occurs in an infinitesimally small sub-interval
โข We count occurrences, not non-occurrences
Key Properties:
โข Mean = ฮป, Variance = ฮป (mean equals variance is a hallmark of Poisson)
โข For large ฮป (typically > 10), Poisson approximates Normal N(ฮป, ฮป)
โข Poisson is the limit of Binomial when n is large and p is small
The Poisson distribution is a discrete probability distribution that models the number of events occurring in a fixed interval of time or space, given a known constant mean rate.
Conditions for Use:
โข Events occur independently of each other
โข The average rate ฮป is constant over the interval
โข At most one event occurs in an infinitesimally small sub-interval
โข We count occurrences, not non-occurrences
Key Properties:
โข Mean = ฮป, Variance = ฮป (mean equals variance is a hallmark of Poisson)
โข For large ฮป (typically > 10), Poisson approximates Normal N(ฮป, ฮป)
โข Poisson is the limit of Binomial when n is large and p is small