91 What do $\pi$ and $e$ stand for in the normal distribution formula? 66 Why does the first 100,000 zeroes of the Riemann Zeta function have double-digit sequence count discontinuities at 00,11,22,33,44,55,66,77,88,99? 58 Find the average of $\sin^{100} (x)$ in 5 minutes? 47 Proving that $1$- and $2D$ simple symmetric random walks return to the origin with probability $1$ 37 Probability of 3 people in a room of 30 having the same birthday

### Reputation (20,756)

 +10 Is there a closed-form equation for $n!$? If not, why not? +10 Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$ +10 $C(n,p)$: even or odd? +10 Show that any two consecutive odd integers are relatively prime

### Questions (3)

 22 What's the minimum of $\int_0^1 f(x)^2 \: dx$, subject to $\int_0^1 f(x) \: dx = 0, \int_0^1 x f(x) \: dx = 1$? 18 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 (226)

 470 probability × 108 124 number-theory × 29 254 combinatorics × 70 119 probability-theory × 20 168 elementary-number-theory × 31 115 normal-distribution × 10 157 probability-distributions × 28 103 pi × 3 133 sequences-and-series × 23 91 algebra-precalculus × 20

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