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.
Best,
wirefree
Appreciate the prompt response, CB.
The suggested solution employing binomial does not address my query. As mentiond in my post, I am attempting to ascertain the time till my next hole-in-1 and not the number of hole-in-ones. Hence, the reference to the "waiting time" distribution.
Would appreciate assistance with regards to my query.
Best,
wirefree
Appreciate your patience, CB. You have a beautiful mind.
As suggested, I arrive at 0.06492057290 chance of Hole-in-1 in the next 870 shots on evaluating poisson by:
The above differs from the result arrived at by evaluating:
...which comes to 0.0672331480. This latter results from the following:
Could you please attempt to explain the difference in methodologies. Being math-junior I grasp the understanding better as explained in the quote above.Now 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. Hence, P(W > t) = e^–lt. Furthermore, the cumulative distribution of W is F(t) = P(W < t) = 1 – e^–lt.
Best,
wirefree
Appreciate the assistance, CB.
As a further exercise in fine-tuning, the formula should be reflective of the game of golf where lesser the number of shots I hit, better the player I am. And better the player, better his chances of a hole-in-1.
So, in the formula above, increasing 870 to 1000 although implies a better chance of a hole-in-1, it is lacking in the obvious places.
Could you suggest a method to address this concern?
Best regards,
wirefree