if we're explicitly using a and b, it's better to make these function parameters, p.random = function(a,b) {... and then bootstrap them with one line for each variable, rather than using arguments.length, like:

a = a || 0;
b = b || 1;

also looks like your text editor decided to use tabs instead of 2 spaces for indentation, can that be fixed?

Yes, even though I chose 2 spaces, apparently if I copy & paste from source that has tabs, those tabs are maintained, but only when I commit the changes. Apparently.

I added parameters a and b, but there is no escaping the use of arguments.length . Note that b = b || 1; would screw up any any range ending with zero.

with named arguments, we can simplify a little more:

if (arguments.length === 1) {
  b = a;
  a = 0;
} else {
  a = a || 0;
  b = b || 1;
}

You cannot do b = b || 1; ! That well mess up invocations like random(-5, 0);

that is a good point. But we can do b = (typeof b !== 'undefined') ? b : 1 (really wish there was a pragma that made truthiness easier in JS in that respect...)

No need to rely on operator typeof for parameter variables. We can test for 'em directly.
Also, it's much safer to catch null as well by using != instead of !==:
b = b != null? b : 1 or b = b != undefined? b : 1 or b = b != void 0? b : 1

Other alternatives:
b = b == null && 1 || b or b = b == undefined && 1 || b or b = b == void 0 && 1 || b

Or even the good old if ():
if (b == null) b = 1 or if (b == undefined) b = 1 or if (b == void 0) b = 1

Yep, the different ways to it correctly is only slightly less than all the ways to do it incorrectly. So I'm leaving my second iteration as is.