## [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] 2016 Putnam Problem B1

2016 Putnam B1. Let be the sequence such that and for , (as usual, the function is the natural logarithm. Show that the infinite series converges and find its sum.

## 2016 Putnam Problem B1

2016 Putnam B1. Let be the sequence such that and for , (as usual, the function is the natural logarithm. Show that the infinite series converges and find its sum.

## [Soln] 2015 IMC Day 1 Problem 2

2015 IMC 1.2. For a positive integer , let be the number obtained by writing in binary and replacing every with and vice versa. For example, is in binary, so is in binary, therefore . Prove that When does equality … Continue reading

## 2015 IMC Day 1 Problem 2

2015 IMC 1.2. For a positive integer , let be the number obtained by writing in binary and replacing every with and vice versa. For example, is in binary, so is in binary, therefore . Prove that When does equality … Continue reading