tag:blogger.com,1999:blog-3891434218564545511.post6945696644232203907..comments2024-03-28T19:56:42.305-05:00Comments on Alexander Pruss's Blog: Missing the center of the target with infinitely many arrowsAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-3891434218564545511.post-45621743735195156952016-04-19T21:23:46.361-05:002016-04-19T21:23:46.361-05:00How many arrows would it take to demonstrate this ...How many arrows would it take to demonstrate this to a confidence level of 90%? Dagmara Lizlovshttps://www.blogger.com/profile/14744785407281199347noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-18374629149385202092016-04-18T21:28:12.293-05:002016-04-18T21:28:12.293-05:00It's even more of a problem with my Galeforce ...It's even more of a problem with my Galeforce crossbow and the bolts I use. I have to have use several different points on the target when shooting because they group so tightly. This is with field points. Hunting. broadheads might yield a different result.Dagmara Lizlovshttps://www.blogger.com/profile/14744785407281199347noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-64617282568715940612016-04-18T15:17:35.760-05:002016-04-18T15:17:35.760-05:00And it's guaranteed that there will be some Ro...And it's guaranteed that there will be some Robin Hoods.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-56695464570303831882016-04-17T20:26:44.940-05:002016-04-17T20:26:44.940-05:00That many arrows grouped so tightly is awfully har...That many arrows grouped so tightly is awfully hard on the fletching. :-)Dagmara Lizlovshttps://www.blogger.com/profile/14744785407281199347noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-82244754355539031832016-04-17T20:21:18.323-05:002016-04-17T20:21:18.323-05:00This comment has been removed by the author.Dagmara Lizlovshttps://www.blogger.com/profile/14744785407281199347noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-86192915303135675572016-04-06T09:24:21.966-05:002016-04-06T09:24:21.966-05:00No, that's not what I had in mind. What I had ...No, that's not what I had in mind. What I had in mind is basically this: Take an uncountable collection of independent random variables uniformly distributed over [0,1]. Is there a canonical answer to the question: What is the probability that NONE of them takes the value 0?<br /><br />This is not meant to be a mathematically precise question. Basically, the question is: How to make this a mathematically precise question?<br /><br />There are at least two difficulties with the question.<br /><br />1. The event "None of the variables takes the value 0" is not measurable in the product measure when the number of variables is uncountable.<br /><br />2. The mathematical understanding of a "uniform" distribution is not sensitive to sets of measure zero, like { 0 }. Thus, you can have a variable that counts as having a uniform distribution on [0,1] but that is guaranteed not to take the value 0 (or not to take a rational number value, etc.). And no matter how many independent variables guaranteed not to take the value 0 you have, it's still guaranteed that none of them take the value 0.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-35584902372449259392016-04-05T22:50:14.023-05:002016-04-05T22:50:14.023-05:00How about this? A density D of arrows means by def...How about this? A <i>density</i> D of arrows means by definition Poisson(D) hits at each point, independently for each point. But this may not be what you have in mind.IanShttps://www.blogger.com/profile/00111583711680190175noreply@blogger.com