N messages are sent to N computers. The messages get mixed up and are distributed randomly. What is the mean number of messages received? [Consider N = 3 ]

Question

nincompoop · Answer

if three messages are randomly sent to three computers, it will be 3 x 3 
but since you are looking for the mean, that would be 9/3

anonymous · Answer

I don't really understand why did you say 3 x 3 ? Could you please explain further ?

wolfe8 · Answer

Wait so you're sending 3 messages to 3 computers but they get mixed up. So did you plan to send one to each? Is there a constriction as to how many messages are sent to each computer?

anonymous · Answer

That's all there is to the question. Since, it is distributed randomly, i don't think there is a constriction as to how many messages are sent to each computer.

nincompoop · Answer

try MAPPING the scenario
with no restriction of the same message to be sent to different computers
message 1  to computer 1, 2 or 3
message 2  to computer 1, 2 or 3
message 3 to computer 1, 2 or 3
with restriction
create your own

anonymous · Answer

So basically, each message will have 1/3 chance of getting sent to one computer - So how do i do the mean o.O ?

wolfe8 · Answer

I was thinking, if there are no restrictions to how many messages are sent to each computer, couldn't there be an infinite number of messages to at least 1 computer? That's where I'm stuck.

anonymous · Answer

Okay, Maybe i got that part wrong and that distributed randomly actually means one message per computer ! Then how will you proceed ?

wolfe8 · Answer

...if you can only get 1 message per computer then the mean would just be 1...

wolfe8 · Answer

Sorry I can't really help. If there were restrictions I can probably work it out but this is kinda weird. Good luck.

anonymous · Answer

Okay ! Thanks Anyway ! :)

wolfe8 · Answer

You're welcome. :)

nincompoop · Answer

if one message can only be sent to a unique computer, then the scenario changes 
map it again
scenario 1 
message 1 goes to computer 1
message 2 goes to computer 2
message 3 goes to computer 3

scenario 2
message 2 goes to computer 1
message 1 goes to computer 2
message 3 goes to computer 3

scenario 3 
message 1 goes to computer 3

and so on and so forth

nincompoop · Answer

considering that you're doing probability, you might want to consider Little's Law