Lecture 1 - Replacing Probability With Expectation

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Lecture 1 - Replacing Probability With Expectation

BenTAU 03 Nov 2019 09:33

Hi,

In lecture one we saw, after the line "In particular the above holds for a random key. Formally, because:" and the line "Now we can fix such specific m1. Formally, because:", that the probability over sk \ m_1 can be replaced with the expectation. Unfortunately wikidot doesn't allow me the embed a picture.

Why is there an equality there?

Thanks

Re: Lecture 1 - Replacing Probability With Expectation

nbitansky 03 Nov 2019 18:39

Law of total expectation.

Re: Lecture 1 - Replacing Probability With Expectation

BenTAU 05 Nov 2019 11:33

Can you please elaborate? I can't see how it follows from E(X) = E(E(X|Y))

Re: Lecture 1 - Replacing Probability With Expectation

nbitansky 05 Nov 2019 11:57

$\Pr_{sk,m}(Event(sk,m)) = E_{sk,m}(Indicator(sk,m)) = E_{m}E_{sk}(Indicator(sk,m)) = E_m\Pr_{sk}(Event(sk,m))$.
We're going to do things like this quite a lot and you should be comfortable with it and be able to complete the details on your own. As I said, mathematical maturity is the most important prerequisite for the course. You're always welcome of course to ask for clarifications on the forum, but I strongly recommend to try as much as you can to figure it out on your own (things aren't going to get easier)

Last edited on 05 Nov 2019 12:13 by nbitansky Show more