int triggerPin = 2;
double uRandom;
long expect = 40000; // expectation value of randomnumbers --> trigger delay in microsecs  
long trigger_delay;

void setup() {
  pinMode(triggerPin, OUTPUT);
  randomSeed(1234);
}

void loop() {

 // comment out the following line
 // to stop trigger production
 digitalWrite(triggerPin, LOW);  
 digitalWrite(triggerPin, HIGH);


  // the next two lines take around 250us....   
  uRandom = 2147483647. / random(2147483647L) ;
  trigger_delay = (long)(expect * log(uRandom));

  // ... here these 250us are substracted...  
  if (trigger_delay > 250)
    trigger_delay -= 250;
  else
    trigger_delay = 1;


  while (trigger_delay > 0){
   if (trigger_delay > 16383) {
     delayMicroseconds(16383);
     trigger_delay -= 16383;
   }
   else
   {
     delayMicroseconds((unsigned int)trigger_delay);
     trigger_delay = 0;
   }
  }
}