Chebyshev's Inequality

This video provides a proof of Chebyshev's inequality, which makes use of Markov's inequality.

[eduardoescoto]

This video cleared up for me what hours of trying to understand it from lecture and reading my textbook couldn't do! Thank you so much for the great videos!

[ibniamin]

A few minutes video shrunk hours distance between me and ChebyShev's. Thank you!!

[SpartacanUsuals]

Hi, I'm glad you liked it! I am planning to continue with these videos. If you have any specific requests however, please let me know! Thanks,
Ben

[saiabineshnatarajan]

A great resource to avoid the hassle of loooking up the textbook or your own notes..
Nailed Chebychev in 3 minutes.. Respected Sir!

[JamesCPinkerton]

You should mention that in Markov's inequality, X is a non-negative random variable.

[davidfield]

I literally watched 10 other videos to find an intuitive proof of chebyshevs inequality until I finally found this video. This video was great.

[SpartacanUsuals]

Hi, glad to hear the videos have reached you over there! Ok - I will definitely be covering maximum likelihood in the next few weeks, and will also be covering monte carlo methods and ratio tests at some point as well. I will see what I can do re: rejection sampling! If you subscribe to me you should get notified when I put the new videos up. Best, Ben

[samshithadevi]

Thanks for the clarity
p([x-m]>=a) is a two sided equation which has >= in the middle, so squaring both sides will give to p([x-m]^2>=a^2). so we can use either equation to plug in the final equation.Well this is my understanding, and if it is correct then your explanation is "Crystal Clear for Me"

[geostat]

I had a hard time following this one back in my undergraduate days in the University of the Philippines. Now it makes sense! 

[SpartacanUsuals]

Very clear even to me in SA. Sadly download speed is slow but not much that you can do about that.

[afifkhaja]

I'm an undergrad stats major at UIC, so I'll be taking a lot of mathematical statistics courses in my final year. A few topics we'll be covering are: rejection sampling, monte carlo methods, maximum likelihood estimation, and ratio tests, I'll let you know if more topics come up. Thank you!!!

[aaronz]

Thank you for making this video! And please paste your last video address.
You skipped a step I think is worth to add E^2(x)<=E(x^2) otherwise it can cause misleading.

[SpartacanUsuals]

Hey, you are nearly there. It is actually because of the modulus sign around the x-m. Imagine that m is the number 1, and a is 2. There are two ways that the difference between x and m can be greater than or equal to 2. Either x is greater than or equal to 3, or x is less than or equal to -2. These two situations are captured by squaring both sides. If is less than -2 then x minus m squared is greater than or equal to 9 for example. Similarly if x is greater than 3.

[haneulkim]

Thanks for amazing video! Any book recommendation on statistics guys?

[Kurtlane]

Somebody – anybody – please write or tell somebody to write a biography (a book) of Pafnuty Chebyshev. I cannot find any book in either English or Russian. And please, whoever writes it, go easy on his facts of life, but heavy on the math, while still approachable for a general reader.
 
He was a major mathematician. It's a pity there is no decent-size biography about him.

[afifkhaja]

Fantastic video! Your explanations are very clear and concise. Please continue making videos on mathematical statistics.

[MrKdes]

how would you derive it without using markovs inequality.

ie through V(X)= E(X-E(X))^2

[ducnguyen]

Thank you a lot, this video helped me so much

[samshithadevi]

Again a Very good video, but again i have i question!, how on earth was p([x-m]>=a) and p([x-m]^2>=a^2) are equal. OH it makes me feel statistics is not about maths but about magic!. Could you elaborate a little more on this.
Thanks in Advance

[elfadlaouielfadel]

machaallah, meaningful analysis, well done