Carl Morris
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 Dec15 awarded Caucus Sep30 awarded Explainer Sep17 awarded Yearling Aug27 revised Linearity In Linear Algebra Cleaned up formatting and added a missing $\alpha$. Aug27 suggested approved edit on Linearity In Linear Algebra Aug26 comment Strictly concave up implies non negative 2nd derivative The proofs I am familiar with, such as from Schramm's Introduction to Real Analysis, uses the Taylor series approximation. Aug26 answered Do mathematics researchers regularly solve problems like this? Aug26 revised process of summing series Added MathJaX dollar signs Aug26 suggested approved edit on process of summing series Aug26 answered Markov property for discrete Markov chains. A question about “adjacent random variables” Mar13 comment Tricks. If $\{x_n\}$ converges, then Cesaro Mean converges (S.A. pp 50 2.3.11) I appreciate your curiosity. I will need a to think through this, and answer your revised questions soon. Research meetings this week, have me busier than usual. Mar10 comment Tricks. If $\{x_n\}$ converges, then Cesaro Mean converges (S.A. pp 50 2.3.11) @TuckerRapu, You are correct that I made a typo around the word "regular". I am not 100% clear on the inequality you are referring to in question 5, so please let me know if I did not address your question. I am also not completely clear on what you mean by "We can't just choose whatever we want?". Mar10 revised Tricks. If $\{x_n\}$ converges, then Cesaro Mean converges (S.A. pp 50 2.3.11) added 1422 characters in body Mar10 revised Tricks. If $\{x_n\}$ converges, then Cesaro Mean converges (S.A. pp 50 2.3.11) added 1422 characters in body Mar5 answered Tricks. If $\{x_n\}$ converges, then Cesaro Mean converges (S.A. pp 50 2.3.11) Sep17 awarded Yearling Feb13 answered Show that each of the following equations has a solution of the form $u(x,y) = f(ax+by)$ for a proper choice of constant $a,b$. Feb10 comment The Probability of an event occuring an exact amount of times Think about how you answered question 1, and you will see that $\binom{40}{2}$ is not giving the same information. If exactly 2 people share the same birthday, that means that the remaining 38 people must have different birthdays from each other and from the two who have the same birthday. Think of a simpler case where you have three people, can you answer the question then? Feb10 answered The Probability of an event occuring an exact amount of times Feb10 comment The Probability of an event occuring an exact amount of times If there are 40 people in the room, then there are anywhere between 1 birth day in the room (everyone has the same birthday) and 40 birth days in the room (everyone has a different birthday). Having only two people sharing the same birthday is the same as saying there are exactly 39 brithdays in the room.