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=X1+X2..+X10

Y2=X1+X2..+X10

...

Y6=X1+X2..+X10

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..