The Characteristic Function of a Normal Random Variable - part 3 (advanced)

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  1. Ben Lambert
  2. Characteristic Function
  3. Statistics (Field Of Study)
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Комментарии
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I think is better to mention the levy's continuity theorem, which states the bijection between probability distribution and characteristic function is sequentially continuous.

mkkkk
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Hi, thank you very much for the video! I just don't understand why the first part integrates to - sqrt(2pi), if you could elaborate on that it would be very helpful :)

vanpr
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Hi Ben, Nice exposition of the complex integration. Thanks for showing explicitly what is really going on in the presence of a complex variable (explanation which is often omitted in showing the proof). I was wondering how the 2nd and 3rd terms integrate to 0. In particular, how to find anti-derivative to the complex function exp{-(S^2)/2}? Thanks.

econessex
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In the fourth part we have -alpha -i*t in the lower bound, not alpha -i*t. Great video by the way

tradingmogador