#### user366312

##### New member

- Joined
- Apr 12, 2019

- Messages
- 3

How does the above equation make sense in case of a Poisson process?

Why is \(\displaystyle (N_3=4)=(N_4−N_1=4)\)?

Can anyone explain?

- Thread starter user366312
- Start date

- Joined
- Apr 12, 2019

- Messages
- 3

How does the above equation make sense in case of a Poisson process?

Why is \(\displaystyle (N_3=4)=(N_4−N_1=4)\)?

Can anyone explain?

- Joined
- Apr 12, 2019

- Messages
- 3

Thanks for the reply. What I understand is:

1. \(\displaystyle P(N_1=2, N_4=6)\) means "the probability of count of 2 items arriving at step-1, AND 6 items arriving at step-4.

2. \(\displaystyle P(N_1=2, N_4-N_1=4)\) means that "the probability of count of 2 items arriving at step-1 AND the 4 items as the difference of steps 4 and 1.

3. which is same as \(\displaystyle P(N_1=2, N_3=4)\) i.e. "the probability of count of 2 items at step-1 AND 4 items at step-3".

I understand (2) as (1) is represented as a "difference" term in (2).

But, how is (2) and (3) equivalent?

- Joined
- Apr 12, 2019

- Messages
- 3