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Just a note:

We don't know it is only one person.

We don't know it is a guy.

We don't know the physical characteristics of the person or persons.

All we know are:

People are dead.
There is more than one with the same fire arm.
They deceased all had the same caliber bullet.
At present, there is no distinctive connection for all the people shot. (other than opportunity)
Only one shot has been known to be fired in each case.
If there is more information the police are not releasing it.
The media is focusing on "the gun".

Good points.

If this is a serial killer, I would expect that within a week he will either be caught, or move his operations, or slow down the pace considerably.

I could see him stopping if the heat gets to be too much, but then picking back up in a month after the publicity dies down.

I'm trying to understand the motivation possibilities if this is a serial killer...

Sexual - I would expect his appetite to be satisfied for a little longer at a time, greater intervals between attacks. Also, would expect the victims to be all women, all men, or couples. This would be Berkowitz.

Megolomania - at some point I would expect him to either try to communicate with the public or press, or step up the "terror" level. Targeting the kid would fit, maybe hitting multiple people at a time at a bus stop or something might be next. But still, I would think he would be taking more time to enjoy the panic. This would be the Zodiac in California.

Delusional/Psycotic - I would think that it would be impossible for him to pull off so many without a trace, if he was really wacked out of his head (thought he was killing demons or something). It just shows too much planning. This would be Richard Allen Chase (Vampire Killer).

Hate/cause- This fits the best to me, where he might just be trying to kill as many "something" as possible, but its not obvious what it is, based on the victims. Could hate Americans, consumers, people with big cars that pollute the environment? This would be the Unabomber, or the link I posted above ("22 Caliber Killer from Buffalo).