This is a beautiful problem form ISI MStat 2017 PSB Problem 3, where we use the basics of Bijection principle and Vandermone’s identity to solve this problem. Problem Consider an urn containing 5 red, 5 black, and 10 white balls. If balls are drawn without...

This problem is an easy application of the basic algorithmic ideas to approach a combinatorics problem using permutation and combination and basic counting principles. Enjoy this problem 3 from ISI MStat 2018 PSB. Problem Consider all permutations of the integers...

This problem is a simple application of the sequential definition of continuity from ISI MStat 2015 PSB Problem 1 based on Telescopic Continuity. Problem- Telescopic Continuity Let \(f: R \rightarrow R\) be a function which is continuous at 0 and \(f(0)=1\)Also assume...

This problem is an easy application in calculus using the basic ideas of curve sketching. This is the problem 1 from ISI MStat 2019 PSB. Problem- curve sketching Let \(f(x) = x^{3}-3 x+k,\) where \(k\) is a real number. For what values of\(k\) will \(f(x)\) have three...

This problem is a cute application of joint distribution and conditional probability. This is the problem 5 from ISI MStat 2018 PSB. Problem Suppose \(X_{1}\) and \(X_{2}\) are identically distributed random variables, not necessarily independent, taking values in...