Let X ¼ Poisson(λ). a. Show that if x is a positive integer, then b. Show that

Let X ˆ¼ Poisson(λ).
a. Show that if x is a positive integer, thenb. Show that if X ˆ¼ Poisson(λ), the most probable value for X is the greatest integer less than or equal to λ. Use part (a) to show that P(X = x) ‰¥ P(X = x ˆ’1) if and only if x ‰¤ λ.

Transcribed Image Text:

Р (X — х) Р(X — х — 1) х