Table of Contents
Dependent and independent clauses | Syntax | Khan Academy
นอกจากการดูบทความนี้แล้ว คุณยังสามารถดูข้อมูลที่เป็นประโยชน์อื่นๆ อีกมากมายที่เราให้ไว้ที่นี่: ดูเพิ่มเติม
Independent clauses can stand on their own as sentences, but dependent clauses can’t. We’ll take a closer look at what this means.
Practice this yourself on Khan Academy right now: https://www.khanacademy.org/syntax/e/dependentandindependentclauses
Watch the next lesson: https://www.khanacademy.org/humanities/grammar/syntax/v/relativeclausessyntaxkhanacademy
Missed the previous lesson? Watch here: https://www.khanacademy.org/humanities/grammar/syntax/v/phrasesandclausessyntaxkhanacademy
Syntax on Khan Academy: Syntax is the ordering of language; it’s the study of how sentences work. In this section, we’ll scratch the surface of syntax as it applies to English grammar. Much more can be said about this subject, but we’ll save that for KA Linguistics.
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Independent Events (Basics of Probability: Independence of Two Events)
An introduction to the concept of independent events, pitched at a level appropriate for the probability section of a typical introductory statistics course. I give the definition of independence, work through some simple examples, and attempt to illustrate the meaning of independence in various ways. (Note: I use the phrase \”not independent\” rather than \”dependent\” almost exclusively. There is nothing wrong with calling events dependent when they are not independent, but I prefer to use \”not independent\” for a couple of reasons.)
(I’m on a bit of a probability run, but looking forward to getting back to statistics videos in the near future.)
This one turned out to be long, as I had a number of points I wanted to discuss. Here’s the breakdown:
0:20. The definition of independence, showing what that means in terms of conditional probability, and some handwaving discussion of what independence means.
3:48. Very simple examples (P(A) = x, P(B) = y, etc.).
6:20. Die rolling examples.
10:03. Discussion of the fact that if A and B are independent, so are (A and Bc), (Ac and B), and (Ac and Bc), including a handwaving justification. The previous example involved a leadin to this. (The handwaving is legit happening behind the scenes.)
11:15. Visual illustration of independence.
14:39. Playing card examples.
18:19. Discussion of how we sometimes assume events are independent (e.g. heads on first toss of a fair coin, heads on second toss), and how this is an assumption, and not something that can be proven mathematically (despite what you might see elsewhere).
19:24. Discussion of how the term \”independent\” can have a different meaning in everyday English compared to its usage in probability, and how that is sometimes a cause for confusion.
Independent and dependent systems | Algebra II | Khan Academy
Independent and Dependent Systems
Watch the next lesson: https://www.khanacademy.org/math/algebra2/systems_eq_ineq/systems_tutorial_precalc/v/practicethinkingaboutnumberofsolutionstosystems?utm_source=YT\u0026utm_medium=Desc\u0026utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/systems_eq_ineq/systems_tutorial_precalc/v/consistentandinconsistentsystems?utm_source=YT\u0026utm_medium=Desc\u0026utm_campaign=AlgebraII
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We’ll again touch on systems of equations, inequalities, and functions…but we’ll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don’t let these big words intimidate you. We’re on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using stateoftheart, adaptive technology that identifies strengths and learning gaps. We’ve also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channel/UCsCA3_VozRtgUT7wWC1uZDg?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
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