User max1 - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T03:29:17Z http://mathoverflow.net/feeds/user/14702 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/63458/textbooks-to-use-as-reference-for-standard-calculus-and-probability-topics Textbooks to use as reference for standard calculus and probability topics Max1 2011-04-29T18:43:49Z 2011-09-12T02:49:59Z <p>I am currently working on a paper to be submitted to a US journal (addressed primarily to non-mathematicians’ audience) where I use </p> <p>(1) some standard calculus stuff (e.g. limits, Taylor expansions, integration by parts) and (2) some standard probability theory facts (e.g. Central Limit Theorem, Chebyshev’s inequality). </p> <p>What textbooks would you advise me to list as references for these topics so that the readers could find these topics covered there? I am looking for books that are well known in the US (and not hard to access), contain full proofs but are not too hard for non-mathematicians to comprehend? Thank you.</p> http://mathoverflow.net/questions/63055/bridging-uniform-and-mass-distributions "Bridging" uniform and "mass" distributions Max1 2011-04-26T16:03:06Z 2011-05-12T23:56:29Z <p><strong>Foreword. The original formulation of this problem was inaccurate; chamomille and Didier Piau came up with a simple example which would not solve the problem in its accurate formulation. Sorry for my inaccuracy. Below is an edited version.</strong> </p> <p>My goal is to find a family X(a, b) of random variables (continuously) depending on two non-negative parameters a and b . The family should have the following properties:</p> <p>(1) X(a, b) take values in the unit interval [0, 1] for all a, b;</p> <p>(2) For dependent random variables Y(a, b) defined as 1/(a+b*X(a, b)) the expected values E[Y(a, b)] exist; </p> <p>(3) When b/a is close to 0, the distribution of X(a, b) is close to uniform on [0, 1]; </p> <p>(4) When a/b is close 0, the distribution of X(a, b) is close to “mass“ distribution (that is, X(a, b) equals 1 with probability 1).</p> <p>So my goal is to find a family of random variables parameterized by a and b to “bridge” the uniform and “mass” distributions.</p> <p>I tried different parameterizations but was not able to find a parameterization satisfying all conditions (1)-(4).</p> http://mathoverflow.net/questions/63458/textbooks-to-use-as-reference-for-standard-calculus-and-probability-topics/63468#63468 Comment by Max1 Max1 2011-04-30T21:34:20Z 2011-04-30T21:34:20Z Thank you very much, Pete, for your comments. At this time more than 150 members have viewed this page but the only recommended book was the book by Hardy. Are there any other textbooks that I could use as a reference for these specific topics in calculus and probability theory? Thank you. http://mathoverflow.net/questions/63055/bridging-uniform-and-mass-distributions/63062#63062 Comment by Max1 Max1 2011-04-27T14:11:42Z 2011-04-27T14:11:42Z Thank you again, Didier! http://mathoverflow.net/questions/63055/bridging-uniform-and-mass-distributions/63062#63062 Comment by Max1 Max1 2011-04-26T18:18:58Z 2011-04-26T18:18:58Z Thank you, Didier. I should have formulated my goal more accurately to avoid this example. http://mathoverflow.net/questions/63055/bridging-uniform-and-mass-distributions Comment by Max1 Max1 2011-04-26T18:14:54Z 2011-04-26T18:14:54Z Thank you, camomille. I agree. In my original post I missed an additional condition (required for the purpose of my investigation) that would not permit this obvious choice. My fault. Sorry and thank you again.