For any 2 events A and B, P(A⋃B) = P(A) + P(B) - P(A⋂B), For any 3 events A, B, C, P(A⋃B⋃C) = P(A) + P(B) + P(C) -P(A⋂B) - P(B⋂C) - P(A⋂C) + P(A⋂B⋂C), If A1⋂A2 = ∅ → P(A1⋃A2|B) = P(A1|B) + P(A2|B). In a second course (Crypto II) we will cover more advanced cryptographic tasks such as zero-knowledge, privacy mechanisms, and other forms of encryption. The course begins with a detailed discussion of how two parties who have a shared secret key can communicate securely when a powerful adversary eavesdrops and tampers with traffic. tastytrade is not in the business of transacting securities trades, nor does it direct client commodity accounts or give commodity trading advice tailored to any particular client’s situation or investment objectives. 49 0 obj Well, given a particular sample in the universe, a particular end-bit string y. In this course you will learn the inner workings of cryptographic systems and how to correctly use them in real-world applications. 88 0 obj That is, if I sum the probability of all elements X in the universe, what I end up with is the number one. This means that if we sum, well if you look at the probability of the entire universe, basically we get one. Transcript. /Parent 107 0 R endobj Suppose we look at the, set of, of two bit strings So, zero, zero, zero, one, one zero and, one, one And suppose we choose a random, from this set. Crash Course on Basic Statistics Marina Wahl, marina.w4hl@gmail.com University of New York at Stony Brook November 6, 2013. Professor. Okay, so that's one of our tables. endobj 8 0 obj In fact very commonly our universe is going to be simply the set of all n bit strings which here is denoted by zero one to the n. So for example the set zero one squared is the set of all two bit strings which happens to be the string zero, zero, zero one, One, zero, and one, one. There's actually a bias towards December. endobj The number of combinations of n things taken r-at-a-time is defined as the number of subsets with r elements of a set with n elements and is equal to the following equation: Example: How many ways can you draw 6 cards from a deck of 52 cards? Well, the random variable can be either zero or one. (Central Tendency) 29 0 obj Transcript. The existence of this Marketing Agreement should not be deemed as an endorsement or recommendation of Marketing Agent by tastyworks. >> But, I guess that's not, that's not relative to the discussion here. So the values of this random variable are going to be either zero or one. This is why it's called a paradox, because 24 supposedly is a smaller number than you would expect. 13 0 obj To round out the first week of our Options Crash Course, we take a look at option delta - a derivative of the BSM, and the one variable that can measure profit, direction, and probability, … 24 0 obj (Some Related Questions) So, one bit, basically. << /S /GoTo /D (section.2.3) >> A really interesting and in-depth course. Week 1. And I'll tell you that a subset A of the universe is called an event. A and B are said to be independent of each other if they’re unrelated to each other. So basically, it's the probability that xy is=to 00, plus the probability that xy, is=to eleven. To view this video please enable JavaScript, and consider upgrading to a web browser that, Discrete Probability (Crash Course, Cont.). Â© 2020 Coursera Inc. All rights reserved. << /S /GoTo /D [98 0 R /Fit ] >> So you can think of a deterministic algorithm as a function that given a particular input data, M, will always produce exactly the same output, A of M. A randomized algorithm is a little different, in that, as before, it takes the [inaudible] and as input, but it also has an implicit argument called R, where this R is sampled anew every time the algorithm is run. endobj 10 Python Skills They Don’t Teach in Bootcamp. So we get P0 over two +P1 over two But what do we kn-, what do we know about P0 and P1? endobj ways to arrange n elements. Well, so what we do is, basically, because we assume the variables are independent, all we have to do is multiply the probabilities. endobj Try the Course for Free. In other words, if you sample about square root a few times, then it's likely that two of your samples. In variable one, output one When the sample in the universe happens to have its least significant bit set to one. So it's not difficult to see that the answer is exactly, one-fourth because, basically the only way that x is equal to two is if r happens to be 1,1 but the probability that r is equal to 1,1 is basically one-fourth because r is uniform over the set of all two bit stings. Throughout the course participants will be exposed to many exciting open problems in the field and work on fun (optional) programming projects. 64 0 obj Okay? 61 0 obj 97 0 obj Similarly for zero one we'll get p zero over two, for one zero we'll get p one over two And for 1-1, again, the probability that y is=to one, and x is=to one, Well, that's P1 the probability that x is=to one, which is a half, so it's P1 over two. << /S /GoTo /D (chapter.10) >> tastytrade is a real financial network, producing 8 hours of live programming every weekday, Monday - Friday. endobj Now, random variables are fairly intuitive objects. I'm gonna use U between two bars to denote the size of the universe U. (Regression) All Rights Reserved. Basically, we proved that the probability that z is = to zero. �B���!H���y�>&.��� �s�� �Z=^��N���ΐ6��� �^�N���B���ymyU5»gm���SMJQĶ��PuHQ ��2P���v։��X���ܢm��jn�Cy endobj << /S /GoTo /D (chapter.7) >> Now there's only one requirement on this function P, and that is that the sum of all the weights, sum up to one. 81 0 obj Interestingly, people's birthdays are not actually uniform across all 365 days of the year. Probability Part 1: Rules and Patterns: Crash Course Statistics #13. And the probability of the set A is called the probability of that event. So formally we say that the probability that X outputs V, is the same as the probability of the event That when we sample a random element in the universe, we fall into the pre image of V under the function X And again, if this wasn't clear, it's not that important. << /S /GoTo /D (chapter.4) >> So, for example, if, r happens to be 00, then x will be zero+0, which is zero. tastytrade is a trademark/servicemark owned by tastytrade. So given a particular input message, M, it's defining a random variable which is, defining a distribution over the set of a [laugh] possible outputs of this algorithm, given the input, M. So the thing to remember is that the output of a randomized algorithm changes every time you run it And in fact, the algorithm defines a distribution and the set of all possible outputs. And so in this case the variable can output a zero or a one. stream There are n factorial (n!) This provability is exactly one half because there is exactly two elements that have their, lest signify bit equals to zero. Well, by the uniform distribution, that's basically equal to one-fourth. endobj 16 0 obj So the first time we run the algorithm we get one output. Over the years many natural cryptographic constructions were found to be insecure. << /S /GoTo /D (section.2.1) >> 5 0 obj So there exists in [inaudible] I and j such that r I is equal to r j. The first one is what's called the uniform distribution.

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