Poisson probabilities
Find the chance of a certain number of events in a fixed time or space, given their average rate.
The Poisson model counts rare, random events such as emails per hour or typos per page. You only need the average number of events, often written λ (lambda) or μ.
The example: on average 3 customers arrive per minute. What is the chance that exactly 2 arrive in a given minute? It is about 0.2240.
Classic Graphing 84
Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.
Open the DISTR menu (2nd then vars) and pick poissonpdf( with alpha and C.
2ndDISTRvarsalphaCprgmFill in the average 3 and the x value 2. Press down after each.
3▼2▼Select Paste, then press enter to calculate.
enterenter
You should seepoissonpdf(3,2) .2240418077
Natural Scientific 991
Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.
Open the Distribution mode and choose Poisson PD.
MENU76Answer the prompts: x 2, then the average 3. Press = after each.
2=3=
You should seePoisson PD p=0.2240418077
Natural Color Graphing
Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.
Open the Stat mode, then DIST (F5), then POISN (F6), and choose Ppd (F1).
MENU2F5F6F1Choose Var (F1), then fill in x 2 and average 3, pressing EXE after each. Press EXE once more to run it.
F12EXE3EXEEXE
You should seePoisson P.D p=0.2240418077
Classic CAS
Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.
Type poissPdf( by hand, then the average and the count.
poisspdf(3,2)Press enter.
enter
You should seepoisspdf(3,2) 0.224042
Tips
- Natural models ask for x first and the average second. Classic models ask for the average first. Check the prompt names.