COM-417 Advanced Probability and Applications
COM-417 Advanced Probability and Applications
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From Olivier Lévêque
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From Olivier Lévêque
Convolution -
From Olivier Lévêque
Expectation of a random variable -
From Olivier Lévêque
Basic properties of expectation -
From Olivier Lévêque
Characteristic function -
From Olivier Lévêque
Random vectorsWatch out three small bugs:- at the beginning of the video: there is of course nothing new here (this was recorded in March 2020) - around 22:50: (X1,X2)… -
From Olivier Lévêque
Gaussian random vectors -
From Olivier Lévêque
Joint distribution of a Gaussian random vector -
From Olivier Lévêque
Cauchy-Schwarz, Jensen and Chebyshev inequalities -
From Olivier Lévêque
Various types of convergence of sequences of random variables -
From Olivier Lévêque
Almost sure convergence implies convergence in probability -
From Olivier Lévêque
Sigma-fields, sigma-field generated by a collection of eventsHere is a small extra comment regarding the definition of a sigma-field:From the third axiom regarding… -
From Olivier Lévêque
The Borel-Cantelli lemma -
From Olivier Lévêque
The law(s) of large numbers, along with its proof -
From Olivier Lévêque
A remark about the proof of the LLN
