Let X frac14 Poisson( Icirc raquo ) a Show that if x is a positive integer, then b Show that if X frac14 Poisson( Icirc raquo ), the most probable value for X is the greatest integer less than or equal to Icirc raquo Use part (a) to show that P(X x) yen P(X x 1) if and only if x curren Icirc raquo (X ) (X 1)

Question: Let X ¼ Poisson(Î»). a. Show that if x is a positive integer, then b. Show that if X ¼ Poisson(Î»), the most probable value

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

(X ) (X 1)

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