endlessend2525
New member
- Joined
- Dec 19, 2016
- Messages
- 2
I struggle with a problem of conditional probability:
I know that phone calls arrive according to a Poisson process with rate 2.
If I know that up to time t = 1 there is one call only, how likely is it that it arrived after t = 0.75 ?
If I know that up to time t = 1 two calls arrived, how likely is it that the second arrived after t = 0.75 ?
So for the first problem I set that
P(S1>0.75/X(1)=1), with S1S1, the time it takes for the first event to occur, and X(1)X(1), the number of events that occurred up to time 1. But then I don't quite see how to handle it.
I need to use the following information that
[X(1)=1]=[S1⩽1<S2]
I know that phone calls arrive according to a Poisson process with rate 2.
If I know that up to time t = 1 there is one call only, how likely is it that it arrived after t = 0.75 ?
If I know that up to time t = 1 two calls arrived, how likely is it that the second arrived after t = 0.75 ?
So for the first problem I set that
P(S1>0.75/X(1)=1), with S1S1, the time it takes for the first event to occur, and X(1)X(1), the number of events that occurred up to time 1. But then I don't quite see how to handle it.
I need to use the following information that
[X(1)=1]=[S1⩽1<S2]
P(0.75<S1⩽1<S2) / P(S1⩽1<S2)
But I don't quite see the idea behind