Hi! I'm a newbe to this forum, hope you can help!
I'm looking at probability function for the sum of flushes during a fixed hour at night (this would be the sum for a district).
And let's say I measure in 10 min interval, that would make 6 values.
Let's say that I know there are 10 people up during this hour, and each could flush in all of those timeslots then:
Y1 is the sum of flushes for timeslot1,
all X are equal distibuted with p=1/6, and independent
Then Y1 would be Bin(n,p)=Bin(10;1/6) right?
E[Y1]=np = 10*1/6 = 1,6666.. Var[Y1] =np(1-p) = 1,3888..
If I'm looking att a 1hour series,
All Y could have value 0 if no one flushes, and 10 for that matter.
One example of outcome of the first two timeslots
Y1=1 + 1 +...+1
Y2=1 + 1 +...+1
Now to the twist:
If each flushes once and an only once , how to I go about that?
Y1=1+ 0+.. +0
Y2=0+ 0+..+1 (if X1 has been 1 the other must be 0)
All X are independent from each other in the same timeslot (different persons)
But all Y are now dependent since you can and must only flush once
Not knowing what to do I've been fooling around with Hypergeometric Hyp(N,n,m)
and sum of Hypergeometric, saying flush is 1 white ball and the other 5 black.
But I'm on very thin Ice here, I don't know what to do.
How do I get Y2? How do I get Var[Y1]?
E[Y1] would still be 1/6 i guess.
Hope you can help, I read some stocastics a long long (long) time ago..