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Let X âˆ¼ Poisson(Î»).

a. Show that if x is a positive integer, thenb. Show that if X âˆ¼ 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) â‰¥ P(X = x âˆ’1) if and only if x â‰¤ Î».

a. Show that if x is a positive integer, thenb. Show that if X âˆ¼ 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) â‰¥ P(X = x âˆ’1) if and only if x â‰¤ Î».

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