Michael Lugo
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12,701
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 68 What do $\pi$ and $e$ stand for in the normal distribution formula? 44 Find the average of $\sin^{100} (x)$ in 5 minutes? 30 Proving that 1- and 2-d simple symmetric random walks return to the origin with probability 1 30 Can you answer my son's fourth-grade homework question: Which numbers are prime, have digits adding to ten and have a three in the tens place? 26 If a prime number is reversed, and then appended to itself, why is the result always a composite number?

### Reputation (12,701)

 +10 Prove that $\sum\limits_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$? +20 Which number is greater, $11^{11}$ or $9^{12}$? +10 Finding $\lim\limits_{n \to \infty}{\frac{1^1+2^2+3^3+\cdots+n^n}{n^n}}$ +10 How to find the distance between a point and line joining two points on a sphere?

### Questions (3)

 18 What's the minimum of $\int_0^1 f(x)^2 \: dx$, subject to $\int_0^1 f(x) \: dx = 0, \int_0^1 x f(x) \: dx = 1$? 14 What do all the $k$-cycles in $S_n$ generate? 2 A nice expression for $P(X>Y, X>Z)$ where $X$ is standard normal, $Y, Z$ are normal with mean 1 and variance 1?

### Tags (152)

 306 probability × 63 82 probability-theory × 11 132 combinatorics × 37 78 normal-distribution × 5 117 elementary-number-theory × 15 76 number-theory × 14 108 probability-distributions × 16 70 algebra-precalculus × 12 98 sequences-and-series × 18 68 pi

### Accounts (16)

 Mathematics 12,701 rep 22658 MathOverflow 8,754 rep 33463 Cross Validated 361 rep 18 Area 51 336 rep 4 Stack Overflow 101 rep 2