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This question already has an answer here:

What is a good approach to proving this inequality:

$$\dfrac{4^m}{4\sqrt{m}}\le\binom{2m}{m}$$

using the Chebyshev inequality: https://en.wikipedia.org/wiki/Chebyshev's_inequality

I thought about using a random variable which has a binomial distribution, but im not sure.

Thank you!

EDIT: It is important to solve it only using Chebychev inequality

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marked as duplicate by Dietrich Burde, Rohan, Alex M., Behrouz Maleki, Jack D'Aurizio Dec 28 '16 at 14:46

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  • $\begingroup$ thank you, but this answer is not using chebyshev... $\endgroup$ – user3720340 Dec 28 '16 at 10:50
  • $\begingroup$ It is, but there are different Chebyshev inequalities, e.g. this one, or this one. Which one do you mean? $\endgroup$ – Dietrich Burde Dec 28 '16 at 10:57
  • $\begingroup$ the second. thanks! $\endgroup$ – user3720340 Dec 28 '16 at 11:26

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