Download Poisson Distribution

QUESTIONS:
2014; 2b, 3c
2013; 2aii, 2bi
Poisson DISTRIBUTION
λxe-λ
P(X = x) =
x!
Used for discrete radom
variables within a given time
interval or spatial area
for instance p(X > 3)
For poisson distribution to be applicable the situation
must meet the following conditions:
The parameter of poisson distribution is:
λ = mean or expected value
Variables must be discrete (not continuous)
Formulae for poisson distribution are given
in the formula sheet
The observation time period or spatial area must be
fixed in advance
The expected value is µ = λ
The number of events occuring in each seperate
interval must be independent
The standard deviation is σ = √λ
Events cannot occur simultaneously
Remember the mean is proportional to the
time period or spatial area in question
The variance is V(X) = λ
practice Question
The mean number of correct answers a student can guess in a 1 minute online
test with unlimited questions is 14.5. Each right answer occurs independently
and is equally likely to occur at any second of the test.
Calculate the probabilty the student will be able to guess at least 3 correct
answers in the first 30 seconds of the test and justify your choice of distribution.
Step One
Step Two
Choose the apropriate distribution
model and justify your choice
Identify the parameters
Poisson distribution:
The mean for 60 seconds, λ = 14.5
The mean for 30 seconds, λ = 7.25
There is a fixed time interval (30 seconds)
Use binomial distribution tables in the formula
sheet or a graphics calculator to find the probability
Each event or correct question is
Using tables or Ppd calculator function
independent and events cannot occur
p(X > 3) = 1 - (p(X=0) + p(X=1) + p(X=2))
Variables are discrete
simultaneously
= 1 - (0.000710 + 0.00515 + 0.0187)
= 0.975
Using Pcd calculator function
studytime.co.nz
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p(X > 3) = 1 - p(X < 2)
= 1 - 0.0245
= 0.976