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# I.S.I. Entrance Problems

## ISI MStat Entrance 2020 – Problems and Solutions

Problems and Solutions of ISI MStat Entrance 2020 of Indian Statistical Institute.

## Testing of Hypothesis | ISI MStat 2016 PSB Problem 9

This is a problem from the ISI MStat Entrance Examination,2016 making us realize the beautiful connection between exponential and geometric distribution and a smooth application of Central Limit Theorem.

## ISI MStat PSB 2006 Problem 8 | Bernoullian Beauty

This is a very simple and regular sample problem from ISI MStat PSB 2009 Problem 8. It It is based on testing the nature of the mean of Exponential distribution. Give it a Try it !

## How to roll a Dice by tossing a Coin ? Cheenta Statistics Department

How can you roll a dice by tossing a coin? Can you use your probability knowledge? Use your conditioning skills.

## ISI MStat PSB 2009 Problem 8 | How big is the Mean?

This is a very simple and regular sample problem from ISI MStat PSB 2009 Problem 8. It It is based on testing the nature of the mean of Exponential distribution. Give it a Try it !

## ISI MStat PSB 2009 Problem 4 | Polarized to Normal

This is a very beautiful sample problem from ISI MStat PSB 2009 Problem 4. It is based on the idea of Polar Transformations, but need a good deal of observation o realize that. Give it a Try it !

## ISI MStat PSB 2008 Problem 7 | Finding the Distribution of a Random Variable

This is a very beautiful sample problem from ISI MStat PSB 2008 Problem 7 based on finding the distribution of a random variable. Let’s give it a try !!

## ISI MStat PSB 2008 Problem 2 | Definite integral as the limit of the Riemann sum

This is a very beautiful sample problem from ISI MStat PSB 2008 Problem 2 based on definite integral as the limit of the Riemann sum . Let’s give it a try !!

## ISI MStat PSB 2008 Problem 3 | Functional equation

This is a very beautiful sample problem from ISI MStat PSB 2008 Problem 3 based on Functional equation . Let’s give it a try !!

## Fly trapped inside cubical box | AMC 10A, 2010| Problem No 20

Try this beautiful Problem on Geometry on cube from AMC 10A, 2010. Problem-20. You may use sequential hints to solve the problem.

## Measure of angle | AMC 10A, 2019| Problem No 13

Try this beautiful Problem on Geometry from AMC 10A, 2019.Problem-13. You may use sequential hints to solve the problem.

## Sum of Sides of Triangle | PRMO-2018 | Problem No-17

Try this beautiful Problem on Geometry from PRMO -2018.You may use sequential hints to solve the problem.

## Recursion Problem | AMC 10A, 2019| Problem No 15

Try this beautiful Problem on Algebra from AMC 10A, 2019. Problem-15, You may use sequential hints to solve the problem.

## Roots of Polynomial | AMC 10A, 2019| Problem No 24

Try this beautiful Problem on Algebra from AMC 10A, 2019. Problem-24, You may use sequential hints to solve the problem.

## Set of Fractions | AMC 10A, 2015| Problem No 15

Try this beautiful Problem on Algebra from AMC 10A, 2015. Problem-15. You may use sequential hints to solve the problem.

## Indian Olympiad Qualifier in Mathematics – IOQM

Due to COVID 19 Pandemic, the Maths Olympiad stages in India has changed. Here is the announcement published by HBCSE: Important Announcement [Updated:14-Sept-2020]The national Olympiad programme in mathematics culminating in the International Mathematical Olympiad...

## Positive Integers and Quadrilateral | AMC 10A 2015 | Sum 24

Try this beautiful Problem on Rectangle and triangle from AMC 10A, 2015. Problem-24. You may use sequential hints to solve the problem.

## Rectangular Piece of Paper | AMC 10A, 2014| Problem No 22

Try this beautiful Problem on Rectangle and triangle from AMC 10A, 2014. Problem-23. You may use sequential hints to solve the problem.

# College mathematics

## ISI MStat PSB 2006 Problem 8 | Bernoullian Beauty

This is a very simple and regular sample problem from ISI MStat PSB 2009 Problem 8. It It is based on testing the nature of the mean of Exponential distribution. Give it a Try it !

## ISI MStat PSB 2009 Problem 8 | How big is the Mean?

This is a very simple and regular sample problem from ISI MStat PSB 2009 Problem 8. It It is based on testing the nature of the mean of Exponential distribution. Give it a Try it !

## ISI MStat PSB 2009 Problem 4 | Polarized to Normal

This is a very beautiful sample problem from ISI MStat PSB 2009 Problem 4. It is based on the idea of Polar Transformations, but need a good deal of observation o realize that. Give it a Try it !

## ISI MStat PSB 2009 Problem 6 | abNormal MLE of Normal

This is a very beautiful sample problem from ISI MStat PSB 2009 Problem 6. It is based on the idea of Restricted Maximum Likelihood Estimators, and Mean Squared Errors. Give it a Try it !

## ISI MStat PSB 2009 Problem 3 | Gamma is not abNormal

This is a very simple but beautiful sample problem from ISI MStat PSB 2009 Problem 3. It is based on recognizing density function and then using CLT. Try it !

## ISI MStat PSB 2009 Problem 1 | Nilpotent Matrices

This is a very simple sample problem from ISI MStat PSB 2009 Problem 1. It is based on basic properties of Nilpotent Matrices and Skew-symmetric Matrices. Try it !

## ISI MStat PSB 2006 Problem 2 | Cauchy & Schwarz come to rescue

This is a very subtle sample problem from ISI MStat PSB 2006 Problem 2. After seeing this problem, one may think of using Lagrange Multipliers, but one can just find easier and beautiful way, if one is really keen to find one. Can you!

## Problem on Inequality | ISI – MSQMS – B, 2018 | Problem 2a

Try this problem from ISI MSQMS 2018 which involves the concept of Inequality. You can use the sequential hints provided to solve the problem.

## Data, Determinant and Simplex

This problem is a beautiful problem connecting linear algebra, geometry and data. Go ahead and dwelve into the glorious connection.

# Research Tracks

## Bayes’ in-sanity || Cheenta Probability Series

Listen to a frequentist’s carping over Bayesian school of thinking!

## Laplace in the World of Chances| Cheenta Probability Series

In this post we will be discussing mainly about, naive Bayes Theorem, and how Laplace, developed the same idea as Bayes, independently and his law of succession goes.

## Bayes and The Billiard Table | Cheenta Probability Series

This post discusses how judgements can be quantified to probabilities, and how the degree of beliefs can be structured with respect to the available evidences in decoding uncertainty leading towards Bayesian Thinking.

## Nonconglomerability and the Law of Total Probability || Cheenta Probability Series

This explores the unsung sector of probability : “Nonconglomerability” and its effects on conditional probability. This also emphasizes the idea of how important is the idea countable additivity or extending finite addivity to infinite sets.

## Judgements in a Fitful Realm | Cheenta Probability Series

This post discusses how judgements can be quantified to probabilities, and how the degree of beliefs can be structured with respect to the available evidences in decoding uncertainty leading towards Bayesian Thinking.

## Probability From A Frequentist’s Perspective || Cheenta Probability Series

This post discusses about the history of frequentism and how it was an unperturbed concept till the advent of Bayes. It sheds some light on the trending debate of frequentism vs bayesian thinking.

## Some Classical Problems And Paradoxes In Geometric Probability||Cheenta Probability Series

This is our 6th post in our ongoing probability series. In this post, we deliberate about the famous Bertrand’s Paradox, Buffon’s Needle Problem and Geometric Probability through barycentres.

Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. Again, we are here with the Part 6 of the Arithmetical Dynamics Series. Let's get started.... Consider fix point of $R(z) = z^2 - z$ . Which is the solution of  R(z)...