Math Help - Poisson Process with condition

1. Poisson Process with condition

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!

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

3. Thanks for your reply. Why is this so?

4. I thought you wanted

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

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

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

5. 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.