Get motivated… try this quiz

Understand the problem

Arithmetic mean and Geometric mean are useful algebraic tools. They have beautiful geometric interpretation as well. The following video takes a tour into the ideas.

Tutorial Problems… try these before watching the video.

1. Show algebraically that \( \frac{a+b}{2} \geq \sqrt {ab} \) if a, b are non negative real numbers. 2. Can you extend the above result to four number? You may send solutions to support@cheenta.com. Though we usually look into internal students work, we will try to give you some feedback.

Now watch the discussion video

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Similar Problems

Balls-go-round |ISI MStat PSB 2013 Problem 10

This is a very beautiful sample problem from ISI MStat PSB 2013 Problem 10. It’s based mainly on counting and following the norms stated in the problem itself. Be careful while thinking !

ISI MStat PSB 2005 Problem 5 | Uniformity of Uniform

This is a simple and elegant sample problem from ISI MStat PSB 2005 Problem 5. It’s based the mixture of Discrete and Continuous Uniform Distribution, the simplicity in the problem actually fools us, and we miss subtle happenings. Be careful while thinking !

polynomials

ISI MStat PSB 2012 Problem 2 | Dealing with Polynomials using Calculus

This is a very beautiful sample problem from ISI MStat PSB 2012 Problem 2 based on calculus . Let’s give it a try !!

ISI MSTAT PSB 2011 Problem 4 | Digging deep into Multivariate Normal

This is an interesting problem which tests the student’s knowledge on how he visualizes the normal distribution in higher dimensions.

Central-Limit-Theorem

ISI MStat PSB 2012 Problem 5 | Application of Central Limit Theorem

This is a very beautiful sample problem from ISI MStat PSB 2012 Problem 5 based on the Application of Central Limit Theorem.

ISI MStat PSB 2007 Problem 7 | Conditional Expectation

This is a very beautiful sample problem from ISI MStat PSB 2007 Problem 7. It’s a very simple problem, which very much rely on conditioning and if you don’t take it seriously, you will make thing complicated. Fun to think, go for it !!

ISI MStat Entrance Exam books based on Syllabus

Are you preparing for ISI MStat Entrance Exams? Here is the list of useful books for ISI MStat Entrance Exam based on the syllabus.

ISI MStat PSB 2008 Problem 8 | Bivariate Normal Distribution

This is a very beautiful sample problem from ISI MStat PSB 2008 Problem 8. It’s a very simple problem, based on bivariate normal distribution, which again teaches us that observing the right thing makes a seemingly laborious problem beautiful . Fun to think, go for it !!

ISI MStat PSB 2004 Problem 6 | Minimum Variance Unbiased Estimators

This is a very beautiful sample problem from ISI MStat PSB 2004 Problem 6. It’s a very simple problem, and its simplicity is its beauty . Fun to think, go for it !!

ISI MStat PSB 2004 Problem 1 | Games and Probability

This is a very beautiful sample problem from ISI MStat PSB 2004 Problem 1. Games are best ways to understand the the role of chances in life, solving these kind of problems always indulges me to think and think more on the uncertainties associated with the system. Think it over !!