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 ChidoriPOWAA August 26th, 2013 12:45 PM

Simple Probability Question

Let $X \sim Po(3)$

I want to find the smallest integer x so that $P(X \geq x) \leq 0.05$.

I started like this: $0.05 \geq P(X \geq x)= 1 - P(X < x), \; P(X=<x) \geq 0.95=$

but here the teacher's answer said: $0.05 \geq P(X \geq x)= 1 - P(X \leq x-1), \; P(X \leq x-1) \geq 0.95.$

Why is this better? Is it because the Poisson distribution is discrete? Or is there something arithmetically I've missed?

 mathman August 26th, 2013 02:56 PM

Re: Simple Probability Question

X ? x-1 is equivalent to X < x, when x and X are integers.

The teacher is quibbling.

 ChidoriPOWAA August 26th, 2013 03:02 PM

Re: Simple Probability Question

Alright, thanks!

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