Watching the video about the link between the indicator function and probability, and then watching this video, is what allowed me to finally make sense of the markov inequality. Thanks for posting!
Hi, Thanks for your message. I have now made a video (which is next in the series) which explains the connection between the expectation of an indicator function and the probability of the event occurring. I have put the link in the video description, and in a message to you. Let me know your thoughts (and feel free/mildly obligated) to like it :) Let me know if you have any further questions, and I will do my best to respond. Best, Ben
Hi, I'm not I quite understand your question. Are you referring to the indicator function? If so, I have made a video explaining the link between the expectations operator and the indicator function. There is a link to it in the description. If you have any further questions please feel free to get in touch. Ben
As far as I'm concerned I REALLY like that you stay on one screen the whole time. I remember images, so scrolling or changing page is always harder to remember for me. :)
I am a student of IIT, one of the premier institutes of India, and still the profs here were not able to make me understand this thing through the entire semester, what you actually did in 5 minutes.
This video lesson is more understandable and shorter than the lecture by my graduate level Statistics teacher. Sad for my school, but good for you! Thank you for posting.
Dear Ben Lambert The explanation was really good, however i could not understand the last step, where the expectation was written in terms of probability (4:59 time of video). Could you please show with some examples here how Expectation and probability are same for the last step as this is the basis for understanding Chebyshev's inequality and then for law of large numbers Thanks in Advance
Hi Paula, yes the Markov inequality only holds for non-negative functions. Simple counter-example: Let X be a normal distributed random variable (mean 0, variance 1). The E(X) would be 0, but P(X>a) would be positive for every a. So the Markov Inequality would not hold for a function which can take negative values.
Why is x on the right side and what is E[x], the expected value? Is it the probability that the function is at X for some probability distribution? Nevermind, I get it much better from your intuition video.
Hi, thanks for your comment. Yes, technically there should have been a less than or equals sign there since x can be zero. Thanks, Ben
Amazing proof. Thanks you. For those who are confused: x >= 0 is a condition for the Markov inequality. So our indicator function need to be >= 0.
Watching the video about the link between the indicator function and probability, and then watching this video, is what allowed me to finally make sense of the markov inequality. Thanks for posting!
Hi, Thanks for your message. I have now made a video (which is next in the series) which explains the connection between the expectation of an indicator function and the probability of the event occurring. I have put the link in the video description, and in a message to you. Let me know your thoughts (and feel free/mildly obligated) to like it :)
Let me know if you have any further questions, and I will do my best to respond.
Best,
Ben
7 years late, but for what it's worth this was helpful to me hahaha
I have a confusion. You wrote " i) a1(x>a)=0
1(x>a) is the notation for this indicator function that gives 0 for xa. So what he wrote is correct.
6 years have passed. Hey, X >=0 because this is the condition for the markov inequality
Hi, I'm not I quite understand your question. Are you referring to the indicator function? If so, I have made a video explaining the link between the expectations operator and the indicator function. There is a link to it in the description. If you have any further questions please feel free to get in touch. Ben
As far as I'm concerned I REALLY like that you stay on one screen the whole time. I remember images, so scrolling or changing page is always harder to remember for me. :)
I am a student of IIT, one of the premier institutes of India, and still the profs here were not able to make me understand this thing through the entire semester, what you actually did in 5 minutes.
Nice video, but keep in mind that a and X need to be positive!
why X and a need to be positive?
ok, that's the definition
2:44 in i), your bound for the case when the indicator function is 0 should be 0
Thanks for your comment - if you have any requests regarding topics you would like to be covered in these videos - please let me know. Thanks, Ben
This video lesson is more understandable and shorter than the lecture by my graduate level Statistics teacher. Sad for my school, but good for you! Thank you for posting.
ONE OF THE BEST EXPLANATION ONNLINE! THANK U
The X is a very special distribution. Why the conclusion from that X can be used to expect all of other distribution's probability in the world？
Thank you so much Mr. Lambert for sharing your knowledge. Much appreciated, and bless you.
You saved my life!!!!thank you sooooooo much👍
Hi Ben, @2:46, you were talking about region a1x
Wow that was very simple and intuitive, thanks
Dear Ben Lambert
The explanation was really good, however i could not understand the last step, where the expectation was written in terms of probability (4:59 time of video). Could you please show with some examples here how Expectation and probability are same for the last step as this is the basis for understanding Chebyshev's inequality and then for law of large numbers
Thanks in Advance
Hello Ben! Thanks for your tutorial! On question: is the Markov's Innequality only valid for non negative X?
Hi Paula, yes the Markov inequality only holds for non-negative functions. Simple counter-example: Let X be a normal distributed random variable (mean 0, variance 1). The E(X) would be 0, but P(X>a) would be positive for every a. So the Markov Inequality would not hold for a function which can take negative values.
Forgive me for not seeing this but why in part ii) section of the function does it have to be that a is less than or equal to x
Thank you very much, this was a very concise and clear explanation.
Why is x on the right side and what is E[x], the expected value? Is it the probability that the function is at X for some probability distribution?
Nevermind, I get it much better from your intuition video.
Hi, E[X] is the expected value of the variable X. Hope that is clear now. Best, Ben
im learning about this in my stochastic class and i have no idea where in stochastic processes this comes is handy...
In your video,P(a
at least you should know where is the turning point, rather than reciting in same pace. what is the outcome ?
I think i just fell in love :)
Great explainer thanks!
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super intellect
Thank you !
a1_(x>=a)
hate this weird notation
I know where I am wrong now.
thanks so much :)
So fucking well taughtttttt
perfect
Neat !
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