Arya_verman_052_Poisson_distribution_variance_mean.pptx

for applied maths

1. Presentation on Poisson Distribution-Assumption , Mean & Variance

2. A discrete Probability Distribution Derived by French mathematician Simeon Denis Poisson in 1837 Defined by the mean number of occurrences in a time interval and denoted by λ Also known as the Distribution of Rare Events Poisson Distribution Simeon D. Poisson (1781-1840)

3. Works when binomial calculation becomes impractical (No. of trials>probability of success), Applied where random events in space or time are expected to occur. Deviation indicates some degree of non-randomness in the events Example: Number of earthquakes per year. Poisson Distribution Cont’d…

4. Requirements for a Poisson Distribution

5. Assumptions The probability of occurrence of an event is constant for all subintervals: There can be no more than one occurrence in each interval Occurrence are independent .

6. If the Poisson variable X , then by the formula: P( X = x ) = e -l l x x ! Mean and Variance Mean of P oisson Probability Distribution Variance of P oisson Probability Distribution Or λ = np

7. Mathematical Calculations #If the average number of accidents at a particular intersection in every year is 18. Then- Calculate the probability that there are exactly 2 accidents occurred in this month . Calculate the probability that there is at least one accident occurred in this month.

8. There are 12 months in a year, so l = = 1.5 accidents per month P( X = 3) = = 0.2510 (a) Calculate the probability that there are exactly 2 accidents occurred in this month .

9. (b) Calculate the probability that there is at least one accident occurred in this month. P( X ≥ 1 ) = P(X=1) + P(X=2) + P(X=3) + …. Infinite. So … Take the complement: P(X=0) = 0.223130…