20. Central Limit Theorem

MIT 6.041 Probabilistic Systems Analysis and Applied Probability, Fall 2010
View the complete course: ocw.mit.edu/6-0...
Instructor: John Tsitsiklis
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
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[@raksahv7860]

Thank you Sir, Just wanted to say thank you, for giving me a deeper insight into probability. I studied this from the 1st lecture to this. I will study the last 5 lectures later on.

[@TCS_School]

The same for me, it was an amazing experience in the intuitive understanding of some of probability theory terminology. Also his co-author textbook is so valuable and in the book they gave CLT as the last thing.

[@BoutinMathieu]

An error is made at 21:50, but is then corrected at 23:48.

[@aniruddhnls]

at 15:02 he says the pmf's have approximated to normal. Before at 9:16 he said pmt's do not approximate.????

[@vivekrai1974]

@@aniruddhnls This is because at 9:16 he takes n =8 and at 15:02 he takes n = 16 and more. In a nutshell, (as he explains later), if the distribution is skewed you have to take a larger n to approximate normal distribution.

[@limzphotography4363]

In love with course outline

[@barbazzfoo]

this prof is so good at lecturing

[@Adityarm.08]

+1, i didn't really like statistics, but this lecture series has completely changed it for me.

[@alejandromaciel8031]

godly lecture skills. what a man

[@xueqiang-michaelpan9606]

the puzzle is really good!

[@Starr169]

One of my students suggested a short cut to calculate probability P(Z>2) without using 1-P(Z2) is equal to P(Z

[@shailendrapatil994]

Thats true because we assume a normal distribution and as it is symmetric , the value will be the same

[@nathansherrard4111]

The potential issue is that most normal tables only show Z >= 0, accounting for that symmetry to save table space.

[@aniruddhnls]

at 15:02 he says the pmf's have approximated to normal. Before at 9:16 he said pmt's do not approximate.????

[@demr04]

@@aniruddhnls watch all the lecture. He literally explain that pmf of Bernoulli is a special case

[@Adnan_19946]

Mid point integration is like, we both can’t be right so lets settle on being half wrong each 😂

[@billmichae]

Excellent Prof!!! ElGrecoProf++

[@MohdZaid-cl3cg]

how is standard deviation is f(1-f)..at 19:40 ???

[@mohamedlehbib7116]

It is 9 month later but f(1-f) because we have a binomial distribution with a mean equal to f, so the variance would be f(1-f)

[@teddonaville1151]

i only understood pdf