Poisson Process with condition

**Niall101** · October 29th 2009, 01:01 PM

People arrive with poisson process with Rate 2

Find

(C) P( N(1) = 2 Given N(3) = 6)

For this i Said this was equal to N(2) = 4 and worked it out using formula.

(D) This one is driving me crazy.

P N(1) (Greater than or =) 2 Given N(1) (Greater than or =) 1

Help With D and confirmation on C would be greatly appreciaded. Thanks!

**matheagle** · October 30th 2009, 08:25 PM

Originally Posted by Niall101

People arrive with poisson process with Rate 2

Find

(C) P( N(1) = 2 Given N(3) = 6)

For this i Said this was equal to N(2) = 4 and worked it out using formula.

(D) This one is driving me crazy.

P N(1) (Greater than or =) 2 Given N(1) (Greater than or =) 1

Help With D and confirmation on C would be greatly appreciaded. Thanks!

(d) should be ${P(N(1)\ge 2)\over P(N(1)\ge 1)}$

**Niall101** · November 1st 2009, 09:12 AM

Thanks for your reply. Why is this so?

**matheagle** · November 1st 2009, 07:25 PM

I thought you wanted

$P(N(1)\ge 2)|N(1)\ge 1)$

$={P(N(1)\ge 2,N(1)\ge 1)\over P(N(1)\ge 1)}$

$={P(N(1)\ge 2)\over P(N(1)\ge 1)}$

**Niall101** · November 2nd 2009, 12:56 AM

No it is what i wanted, Just wanted to understand where it came from so I can do similar type question myself in the future. Thanks very much for your replies. Really appreciate it.

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