Poisson

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March 17th 2011, 03:26 PM
dwsmith

Poisson

$\lambda=4$

$\displaystyle P(X\geq 5|X\geq 2)=\frac{P(X\geq 5\cap X\geq 2)}{P(X\geq 2)}=\frac{P(X\geq 5)}{P(X\geq 2)}=\frac{1-P(X<5)}{1-P(X<2)}$

When I did this, the answer was incorrect. Is this process wrong and why?
March 17th 2011, 03:43 PM
pickslides

Looks correct to me. Was your answer even close?

I get $\displaystyle \frac{1-\left(\frac{4^4e^{-4}}{4!}+\frac{4^3e^{-4}}{3!}+\dots +\frac{4^0e^{-4}}{0!}\right)}{1-\left(\frac{4^1e^{-4}}{1!} +\frac{4^0e^{-4}}{0!}}\right)$
March 17th 2011, 03:45 PM
dwsmith

Quote:

Originally Posted by pickslides

Looks correct to me. Was your answer even close?

I get $\displaystyle \frac{1-\left(\frac{4^4}{4!}+\frac{4^3}{3!}+\dots +\frac{4^0}{0!}\right)}{1-\left(\frac{4^2}{2!}+\frac{4^1}{1!} +\frac{4^0}{0!}}\right)$

You forgot $e^{-4}$ , but I obtain .4085 and the answer is .37 somethingish.
March 17th 2011, 03:51 PM
pickslides

Quote:

Originally Posted by dwsmith

You forgot $e^{-4}$ ,

I did forget, but stick by my answer (after the edit!). Sorry dw, might have to wait for another forum member to come through and eyeball the problem.

Maybe the book's answer is wrong?
March 17th 2011, 04:58 PM
awkward

Quote:

Originally Posted by dwsmith

$\lambda=4$

$\displaystyle P(X\geq 5|X\geq 2)=\frac{P(X\geq 5\cap X\geq 2)}{P(X\geq 2)}=\frac{P(X\geq 5)}{P(X\geq 2)}=\frac{1-P(X<5)}{1-P(X<2)}$

When I did this, the answer was incorrect. Is this process wrong and why?

Looks right to me.

I get 0.4086 as the answer.

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