64 Sum of 'the first k' binomial coefficients for fixed n 35 What's your favorite equation, formula, identity or inequality? 34 Suggestions for good notation 33 When are probability distributions completely determined by their moments? 29 When does 'positive' imply 'sum of squares'?

### Reputation (12,064)

 +20 If you break a stick at two points chosen uniformly, the probability the three resulting sticks form a triangle is 1/4. Is there a nice proof of this? +10 When are probability distributions completely determined by their moments? +10 Sum of 'the first k' binomial coefficients for fixed n +10 Combining Correlation Coefficients

### Questions (19)

 70 Teaching statements for math jobs? 68 If you break a stick at two points chosen uniformly, the probability the three resulting sticks form a triangle is 1/4. Is there a nice proof of this? 54 Why are powers of $\exp(\pi\sqrt{163})$ almost integers? 35 Is there a combinatorial reason that the (-1)st Catalan number is -1/2? 29 When are some products of gamma functions algebraic numbers?

### Tags (106)

 251 co.combinatorics × 39 56 ca.classical-analysis-and-odes × 14 161 nt.number-theory × 35 48 soft-question × 19 153 pr.probability × 31 48 graph-theory × 10 74 binomial-coefficients × 2 41 prime-numbers × 9 63 asymptotics × 9 36 st.statistics × 9