# Tag Archives: Probability

## [Soln] Central Limit Theorem: Strange Result!

For , define the random variable Let . Prove that as , a) the distribution of converges to for some real number , b) but converges to 2. (Credits: I learnt of this problem from Persi Diaconis in my probability class.) … Continue reading

## Central Limit Theorem: Strange Result!

For , define the random variable Let . Prove that as , a) the distribution of converges to for some real number , b) but converges to 2. (Credits: I learnt of this problem from Persi Diaconis in my probability class.)

## [Soln] 2013 AIME I Problem 6

2013 AIME I 6. Melinda has three empty boxes and 12 textbooks, three of which are mathematics textbooks. One box will hold any three of her textbooks, one will hold any four of her textbooks, and one will hold any five of … Continue reading

## 2013 AIME I Problem 6

2013 AIME I 6. Melinda has three empty boxes and 12 textbooks, three of which are mathematics textbooks. One box will hold any three of her textbooks, one will hold any four of her textbooks, and one will hold any five of … Continue reading

## [Soln] Variance Problem

With the assumption that prove the following inequality: (This problem was taken from this link.)