How many MIT courses are there with no videos, and Prof. Strang comes through with an incredibly relevant course with full course videos. Amazing.
@georgesadler78303 жыл бұрын
Professor Strang thank you for explaining and analyzing Definitions and Inequalities from probability and statistics. The pictures and examples really help me to understand the quality of this lecture.
@ziqichen46544 жыл бұрын
For chebyshev, on the left hand side, the right bracket should close after ">=a".
@allyourcode3 жыл бұрын
Also, at the end, he was supposed to say that P[Y >= a^2] instead of E[Y]
@1290DR3 жыл бұрын
Mr. Professor - you are great!
@ankits25134 жыл бұрын
You sir are an Inspiration:)
@cyberneticqualanaut72072 жыл бұрын
I can see and prove a covariance matrix with x and y independent is a positive definite matrix. But when x and y are dependent, I don't think the covariance matrix V is positive semidefinite. In the 2x2 case uT*V*u could be less than zero for the case when u = [1; -1] for instance.
@christianjimenez18774 жыл бұрын
Brilliant!!!
@tmusic992 жыл бұрын
I am missing a reference to the population when explaining expected mean and expected variance. Then you sample the population for a sample mean and/or a sample variance.
@rusty-b3p4 жыл бұрын
11:55 when you try to guess answer on multiply choice test
@quanyingliu71685 жыл бұрын
Proof of Markov Inequality: en.wikipedia.org/wiki/Markov%27s_inequality#Proof_in_the_language_of_probability_theory
@1u2t34 жыл бұрын
The example for Markov inequality seems not proper. For sequence 1,2,3,4,5, the mean can be 1 only if P2, P3, P4, P5 are all 0
@seamus98983 жыл бұрын
I agree it's a weird simplified example but the math still checks out
@strahilpastuhov18863 жыл бұрын
P1 need not be 1, so P2 etc. can be above zero and the mean still be 1.
@PrzemyslawSliwinski2 жыл бұрын
@@strahilpastuhov1886 Nope. In this example you have that 2p₂ + 3p₃ + 4p₄ + 5p₅ = 1 - p₁ = p₂ + p₃ + p₄ + p₅. That is, you get p₂ + 2p₃ + 3p₄ + 4p₅ = 0.
@PrzemyslawSliwinski2 жыл бұрын
@@seamus9898 Yup, it is almost like a dice example.
@linelendur Жыл бұрын
Yeah, I paused the video just after he collected terms and tried to move forward myself (by collecting (p1+...+p5) together) and immediately hit this issue. That said, if you replace "1" with E[x] in both example the result he's showing still falls out, as "E[x]/3" instead of "1/3"
@brendawilliams80623 жыл бұрын
Thx.
@ranjit87212 жыл бұрын
In 18.05, the camera movement was very nice. In 18.065, I think the camera person is not that professional.
@sicongliu14849 ай бұрын
What is 18.05? Could you please share the links and I am very interested. Thanks!
@deepaks.m.67093 жыл бұрын
Another useful resource: metacademy.org/graphs/concepts/chernoff_bounds#focus=chernoff_bounds&mode=learn