If X &#x223C;<!-- ∼ --> Poisson <mo stretchy="false">( &#x03BB;<!-- λ --> <mo str

Essence Byrd

Essence Byrd

Answered question

2022-05-01

If X Poisson ( λ ), prove that P [ X = k ] is maximized at k = λ

How would I go about proving something like this so that the method would work to prove a maximization point of other random variables like say Binomial is max at k = ( n + 1 ) p?

Answer & Explanation

Jocelynn Meyer

Jocelynn Meyer

Beginner2022-05-02Added 9 answers

what is P ( X = k ) / P ( X = k + 1 )?
Is
e λ λ
Soo, I think you can handle it on your own
smachttenbem

smachttenbem

Beginner2022-05-03Added 18 answers

The expression will depend on k, and it has the property that it will be less than one if and only if P ( X = k ) < P ( X = k + 1 )

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