A flock of birds living in a tree return to the tree after sun set
at a rate of 5 per minute in accordance with a Poisson process.
If the probability of each bird arriving to the tree is 0.82, find the probability that 12 birds would arrive in three minutes interval
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The Poisson process describes the probability of occurrence of an event within an interval of time. Suppose
X
be a random variable denoting the number of occurrences of an event, the probability of
x
occurrences per unit of time can be expressed as:
P
(
X
=
x
)
=
λ
x
e
−
λ
x
!
, where
λ
is the average occurrence rate in a unit time interval.
Exponential Distribution
Exponential distribution describes the waiting time between Poisson occurrences.
Let
T
be the waiting time between now and the next event. The probability that no event occurs between now and time
t
can be expressed as:
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