(11C) Poisson distribution

[Gamo]

The Poisson distribution is popular for modelling the number of times an event occurs in an interval of time or space.

Formula: P(k events in interval) = (e^-λ)(λ^k) / k!

where:
λ (lambda) is the average number of events per interval
e is the number 2.71828... (Euler's number) the base of the natural logarithms
k takes values 0, 1, 2, …
k! = k × (k − 1) × (k − 2) × … × 2 × 1 is the factorial of k.

Example Problem:
Ugarte and colleagues report that the average number of goals in a World Cup soccer match is approximately 2.5
Because the average event rate is 2.5 goals per match, λ = 2.5
What is the probability of gold of P(k) = 0, 1, 2, 3, 4, 5, 6, 7

Program:

Code:


LBL A (λ)
STO 1
RTN
LBL B (k)
STO 2
RTN
LBL C (P)
RCL 1
CHS
e^x
RCL 1
RCL 2
Y^x
x
RCL 2
X!
/
RTN

Run Program:
2.5 A
0 B
C 0.082
1 B
C 0.205
2 B
C 0.257
3 B
C 0.213
.
.
.
.
7 B
C 0.010

The table below gives the probability for 0 to 7 goals in a match.

k P(k goals in a World Cup soccer match)
0 0.082
1 0.205
2 0.257
3 0.213
4 0.133
5 0.067
6 0.028
7 0.010

Credit to Wikipedia for information and example problem.

Gamo