- A model often used for computing probabilities associated with the number of successes within a time interval of fixed length or within a region of given size.
- Example:
- The number of typing errors per page
- The number of defects in a manufactured article
2.1. Poisson Distribution in R-Programming
- Poisson Distribution formula
- P(x= a) = dpois
- P(x<=a) = ppois
- P(x>a) = 1 - P(x<= a - 1) = 1 - ppois(a-1)
- Suppose that the number of defective screws produced by a sophisticated machine per day has a Poisson distribution with a mean of 2. What is the probability that out of total production of the day, there is:
- No defective screw
- P(x = 0) = dpois(0,2) = 0.1353353
- There is a 13% of probability of no defective screw
- Exactly 2 defective screws?
- P(x = 2) = dpois(2,2) = 0.2706706
- There is a 27% of probability of excatly 2 defective screws
- At most two defective screws?
- P(x <= 2) = ppois(2,2) = 0.6766764
- There is a 67% of probability of at most two defective screws
- At least one defective screw?
- P(x >= 1) = 1 - P(x <= a -1) = 1 - ppois(0,2) = 0.8646647
- There is a 86% of probability of at least one defective screw