I am in love with this channel due to these kind of vids. This is my second my vid of this channel. need to explore more vids. kindly keep uploading these vids with amazing explanation. Kindly suggest a book or else will request you to write one book.
For the third question however, we missed an important point which considering x>= u. Here we had |x-u| >= 0 which has two parts, x-u >= 0 when x>=u and x-u
In our case x=mu as there is only one possible value for x. So x>= mu and mu>=x would simply translate to x=mu. So it would not change the math. In other cases, what you said is true.
For the first question can we just say that to find the %of values between [mu - sigma] to [mu + sigma] is just the integral of Pdf from [mu - sigma] to [mu + sigma]. Which can be between [0% and 100%].
This argument would not work well if the question was about two standard deviations instead of one standard deviation. Chebyshev’s inequality will give a much better bound on the probability than just saying 0-100%
I'm trying to answer second question, I'm thinking Chebyshevs Inequality might fail in Pareto distribution as most of the data concentrate at lower x values.
The distribution need not be Pareto for us to be able to apply Chebyshev’s inequality. Actually there are some Pareto distributions which do not have a finite mean for which we may not be able to apply the inequality.
Then, 1/k^2 would be greater than 1 which makes the inequality trivial as all probabilities have to be less than or equal to 1. Hence the inequality holds whenever K is greater than 0.
I think the ans for last question is it actually fails when we need to predict the output using the parameter because chebeshev inequality is a non- parametric one
Yes, Chebyshev’s inequality is a simple extension of Markov inequality. You can derive Chebyshev from Markov inequality in just 2 to 3 steps. You can find that on the Wikipedia article of Chebyshev’s inequality.
You cannot use this inequality if the mean or standard deviation is non-finite. That is clearly mentioned in the above link that I shared in the formal definition section.
Please check the rest of the video on why this answer is true only if the underlying distribution is Gaussian. Ask yourself what is the underlying distribution is non Gaussian and as we’ve done in the video.
Not much for data scientist roles. You are expected to know the basics of time and space complexity, Recursion along with data structures that are often used in machine learning like hash tables and binary trees. For applied scientist roles, if you come from CS background, you’ll have dedicated rounds for data structures and algorithms very similar to those of software engineers.
What bullshit at 10:00 ? The proper interpretation is for all K's the inequality holds, it means P(X-\mu > 0) ightarrow 0 Please don't spread stupid things on internet.
Please check the Chebyshev's inequality's probabilistic statement here: en.wikipedia.org/wiki/Chebyshev%27s_inequality#Probabilistic_statement It is only valid when k>0 and when we have non-zero variance for X
@@AppliedAICourse so say that. Don't put it in the equation and come up with stupid inequalities. It is like multiplying 0 on both sides of an equation and coming up with ridiculous equations like 3=4. Just mention that the Chebyshev's inequality doesn't work for zero variance. Period.
I think that’s what we tried to convey. May be you misunderstood us. We are trying to show this as a boundary case where Chebyshev’s inequality does not work. I think most other viewers got that point through as no one else raised an issue with this aspect.
