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# Poisson distribution

i aint a lecturer :)

by

Tweet## Dr.Michael Booth Scofield

on 4 December 2012#### Transcript of Poisson distribution

Discrete Probability Continuous Probability Binomial Distribution Poisson Distribution This distribution is used for calculating the possibilities for an event with the given average rate of value(λ). λ - average rate of value.

x - Poisson random variable/ No of events

e - base of logarithm Discrete probability distribution for the counts of events that occur randomly in a given interval of time/ space Mean = λ

St.D = √λ when the sample size is larger a binomial distribution can be described using Poisson distribution Normal Distribution - Examples :

No of messages Kasun receives in a day

No of pages Thilini reads in an hour Reesha Says that the number of Heart attacks in Male city each year can be described as Poisson distribution - ? POISSON DISTRIBUTION Events happen Independently of each other Average Number of events Fixed Interval YES! Large population, Fixed Interval, Independent of each other Number of lectures Ruwini skipped in November No!! Not at all independent,

Not a Fixed interval Q2 : Thilini Says that Births in Kalubowila Hospital occur randomly at an average rate of 1.8 births per an hour

i. Probability of observing 4 births in a given hour at the hospital

ii. Probability of observing 4 or more than 4 births in a given hour at the hospital

iii. Probability of Thilini observing 5 births in a given 2 hours interval When x = 4

1.8 births per hour

e -1.8 = 0.1532

0.1532 x 10.4976

4 x 3 x 2 x 1

= 0.067 4 or more than 4 - 4 to ∞

more than 4 - 5 to ∞

less than 4 - 3,2,1,0

4 or less than 4 - 4,3,2,1,0 λ = 1.8 births per hour

x = No of births (4) ii. x = 4 to ∞

∞ ????? :O

when x = 0

0.1532

when x = 1

0.27576

when x = 2

0.2481

when x = 3

0.1489

p = 1

1 - (0.1532 +0.2757+ 0.2481+0.1489) = 0.1739 iii.

per hour 1.8

2 hours???

1.8 x 2 = 3.6

so the birth rate or λ = 3.6

x or no of events = 5

e (- 3.6) = 0.1236

0.1236 x (3.6)5

5x4x3x2x1

= 0.6228 Q1 : during a laboratory experiment Krishanthi notices that the average number of radioactive particles passing through a counter in 1 ms is 4. what is the probability that 6 particles enter the counter in given 1 ms? λ = 4

0.0183 x 4 (6)

6x5x4x3x2x1

= 0.1041 i. Probability of observing 4 births in a given hour at the hospital ii. Probability of observing 4 or more than 4 births in a given hour at the hospital No of times Ramees knocking his head in july?? Gracious! :) Hola Amigos :)

Full transcriptx - Poisson random variable/ No of events

e - base of logarithm Discrete probability distribution for the counts of events that occur randomly in a given interval of time/ space Mean = λ

St.D = √λ when the sample size is larger a binomial distribution can be described using Poisson distribution Normal Distribution - Examples :

No of messages Kasun receives in a day

No of pages Thilini reads in an hour Reesha Says that the number of Heart attacks in Male city each year can be described as Poisson distribution - ? POISSON DISTRIBUTION Events happen Independently of each other Average Number of events Fixed Interval YES! Large population, Fixed Interval, Independent of each other Number of lectures Ruwini skipped in November No!! Not at all independent,

Not a Fixed interval Q2 : Thilini Says that Births in Kalubowila Hospital occur randomly at an average rate of 1.8 births per an hour

i. Probability of observing 4 births in a given hour at the hospital

ii. Probability of observing 4 or more than 4 births in a given hour at the hospital

iii. Probability of Thilini observing 5 births in a given 2 hours interval When x = 4

1.8 births per hour

e -1.8 = 0.1532

0.1532 x 10.4976

4 x 3 x 2 x 1

= 0.067 4 or more than 4 - 4 to ∞

more than 4 - 5 to ∞

less than 4 - 3,2,1,0

4 or less than 4 - 4,3,2,1,0 λ = 1.8 births per hour

x = No of births (4) ii. x = 4 to ∞

∞ ????? :O

when x = 0

0.1532

when x = 1

0.27576

when x = 2

0.2481

when x = 3

0.1489

p = 1

1 - (0.1532 +0.2757+ 0.2481+0.1489) = 0.1739 iii.

per hour 1.8

2 hours???

1.8 x 2 = 3.6

so the birth rate or λ = 3.6

x or no of events = 5

e (- 3.6) = 0.1236

0.1236 x (3.6)5

5x4x3x2x1

= 0.6228 Q1 : during a laboratory experiment Krishanthi notices that the average number of radioactive particles passing through a counter in 1 ms is 4. what is the probability that 6 particles enter the counter in given 1 ms? λ = 4

0.0183 x 4 (6)

6x5x4x3x2x1

= 0.1041 i. Probability of observing 4 births in a given hour at the hospital ii. Probability of observing 4 or more than 4 births in a given hour at the hospital No of times Ramees knocking his head in july?? Gracious! :) Hola Amigos :)