tag:blogger.com,1999:blog-8890204.post8289467372913299566..comments2022-08-10T05:55:57.894-04:00Comments on My Biased Coin: An Exceptional Exponential EmbeddingMichael Mitzenmacherhttp://www.blogger.com/profile/06738274256402616703noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-8890204.post-66640108601759482862014-07-13T20:51:02.129-04:002014-07-13T20:51:02.129-04:00Hi Mike,
C5838ould you please show why "the ...Hi Mike,<br /><br />C5838ould you please show why "the infinite sums converge with probability 1 and are unequal with probability 1"? Thank you very much.Knightriderhttps://www.blogger.com/profile/10925941573506227858noreply@blogger.comtag:blogger.com,1999:blog-8890204.post-90094444808804541882011-10-26T08:24:14.700-04:002011-10-26T08:24:14.700-04:00Um, p=2, not p=1. (Embarrassed.)Um, p=2, not p=1. (Embarrassed.)Claire Mathieuhttps://www.blogger.com/profile/10957755706440077623noreply@blogger.comtag:blogger.com,1999:blog-8890204.post-19461309877358544962011-10-26T08:11:36.108-04:002011-10-26T08:11:36.108-04:00Hi Mike!
Nice. Here are some pedagogical comments....Hi Mike!<br />Nice. Here are some pedagogical comments.<br /><br />- If I was teaching this, I would do it just for p=1: it's simpler but the argument is the same and it is just as beautiful. Then in the end I would throw in a comment: "Consider this generalization. The proof extends (exercise)." That is, I try to teach the simplest problem whose solution uses the ideas I want to convey. I know that many mathematicians do the opposite (try to see how far the ideas can go, and show the most general result that can be obtained from those ideas), but I find that simpler works better for me.<br /><br />- If I was teaching this, instead of defining the process formally I would do it from example, with concrete values for x and y. "When there are 7 balls in bin 1 and 3 balls in bin 2, the probability that the ball lands in bin 1 is 7/(7+3)=.7 and the probability that it lands in bin 2 is 3/(7+3)=.3." Students can always ask questions if that's not enough to make things clear. <br /><br />- Also, what is missing for a computer scientist's mind such as mine is: Why? Where does this process come from? I almost stopped reading your entry in the middle of the second paragraph because the motivation is missing. Even for a blog entry, a sentence about that would be greatly helpful. <br /><br />By the way, this is a nice post. Enjoyable for me to read. I knew this already, but if you did it with something that I didn't know, it would be great fun, a very nice way to learn a little nugget of science.Claire Mathieuhttps://www.blogger.com/profile/10957755706440077623noreply@blogger.comtag:blogger.com,1999:blog-8890204.post-27477456891956261252011-10-26T01:06:13.928-04:002011-10-26T01:06:13.928-04:00Are you using this as a metaphor for wealth in thi...Are you using this as a metaphor for wealth in this country? :)<br /><br />Dark humor aside, yes, it's a beautiful proof.<b></b>Anonymousnoreply@blogger.com