Michael Lugo
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 60 What do $\pi$ and $e$ stand for in the normal distribution formula? 36 Find the average of $\sin^{100} (x)$ in 5 minutes? 27 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? 26 Proving that 1- and 2-d simple symmetric random walks return to the origin with probability 1

### Reputation (10,658)

 +10 How to evaluate $\log x$ to high precision “by hand” +10 Have I calculated the sum $\sum\limits_{k=1}^\infty\frac{q\lambda^k}{k!e^\lambda}$ correctly? +10 Compute $\sqrt[7]{0.999}$ to three decimal places.(From Gelfand's Algebra text.) +10 $n!+1$ being a perfect square

### Questions (3)

 18 What's the minimum of $\int_0^1 f(x)^2 \: dx$, subject to $\int_0^1 f(x) \: dx = 0, \int_0^1 x f(x) \: dx = 1$? 11 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 (127)

 284 probability × 58 63 probability-theory × 10 115 combinatorics × 32 60 pi 88 elementary-number-theory × 9 59 algebra-precalculus × 10 86 probability-distributions × 14 58 sequences-and-series × 13 67 normal-distribution × 4 52 integration × 6

### Accounts (15)

 Mathematics 10,658 rep 22254 MathOverflow 8,204 rep 33061 Area 51 336 rep 4 Cross Validated 301 rep 18 Stack Overflow 101 rep 2