Viewing the time till my next hole-in-1 in golf as a random variable, I wondered if the recently covered fundamentals of exponential random variables in class, or what was informally referred to as the "waiting time" distribution, could be employed.
NOTE: The probability of an amatuer hitting the ball into the hole from the tee-off is 1/12,500 i.e. once every 12,500 shots.
I have thus far gathered the following framework:
We consider a Poisson process with rate l per unit time and the random variable W, which is the time one must wait to see the next count, given by
P(W < t) = 1 – exp(–l*t)
I crunched in maple the following:
1-exp(-(1/12500)*(87*10)), where 87 is the number of shots I typically hit per round of 18 holes of golf, multiplied by 10 to arrive at the possibly of hitting one in winter break i.e. 10 rounds of golf.
Would appreciate corrections and suggetions to further the train of thought.