1 basic probability concepts suppose we have a process (referred to as a random variab. Probability and entropy engr 76 lecture notes β april 4, 2024 ayfer ozgur, stanford university in this lecture, we revisit the basic notions of probability and define some quantities like entropy that will form the foundation for the upcoming lectures. Mit opencourseware is a web based publication of virtually all mit course content Ocw is open and available to the world and is a permanent mit activity. Aly focuses on probability, covering key concepts such as conditional probability, independent events, and the multiplication law of probability It includes definitions, examples, and calculations to illustrate these concepts.
In this case we introduce the density probability p(a) The product p(a)da gives the probability of finding the values of quantity a in the range between a and a +da. In the appendices, i give some of the basic mathematical concepts that clarify, unify, and simplify some of the ideas that are discussed in informal terms in the lectures. Let us consider an example Suppose x1 is a random variable over 1 = f0 1g such that p [x1 = 0] = 1=2
1g such that p x2 = x1jx1 = x1 = 2=3 Note that x2 is biased towards the outcome of x1 What is the probability that we get p [x1 = 0 We do that by assigning a number to each event (e) called the probability of that event (p (e)) The probability of an event is a number between 0 and 1 (inclusive) If the probability of an event is 0, then the event is impossible
On the other hand, an event with probability 1 is certain to occur. This text is not a treatise in elementary probability and has no lofty goals Therefore, its emphasis is on examples, which are chosen without much redundancy. Explore key probability concepts, including experiments, outcomes, and rules, with practical examples and visual aids for better understanding.
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