This may be a dumb question. The Poisson postulates are: 1. P <mo stretchy="false">(

windpipe33u

windpipe33u

Answered question

2022-04-30

This may be a dumb question.

The Poisson postulates are:

1. P ( n = 1 , h ) = λ h + o ( h )
2. i = 2 P ( n = i , h ) = o ( h )
3. Events in nonoverlapping intervals are independent

What ensures that λ h [ 0 , 1 ] irrespective of the value of λ ?

Answer & Explanation

prstenast4yi

prstenast4yi

Beginner2022-05-01Added 12 answers

What ensures that λ h [ 0 , 1 ] irrespective of the value of λ?

Nothing does, and this is not what these conditions say. Condition 1. should read
P ( N h = 1 ) = λ h + o ( h ) ,
which means
lim h 0 + P ( N h = 1 ) h = λ .
Note that O ( h ) should read o ( h ) and that the condition is only concerned with the limit when h 0 +.

Likewise, condition 2. should read
P ( N h 2 ) = o ( h ) ,
which means
lim h 0 + P ( N h 2 ) h = 0.

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