Introduction to Artificial Intelligence
... • If we assume that each piece of evidence (symptom) is independent given the diagnosis (conditional independence), then given evidence e as a sequence {e1,e2,…,ed} of observations, P(e | di) is the product of the probabilities of the observations given di. • The conditional probability of each indi ...
... • If we assume that each piece of evidence (symptom) is independent given the diagnosis (conditional independence), then given evidence e as a sequence {e1,e2,…,ed} of observations, P(e | di) is the product of the probabilities of the observations given di. • The conditional probability of each indi ...
Lecture 3: The Wave Function
... definite position. The probability density of this superposition state will show no interference because when one of the component wavefunctions exhibits a peak, the other component wavefunction is zero, so their product is zero at all positions. Similarly, ψ6 = ψ3 + ψ4 is a superposition of two stat ...
... definite position. The probability density of this superposition state will show no interference because when one of the component wavefunctions exhibits a peak, the other component wavefunction is zero, so their product is zero at all positions. Similarly, ψ6 = ψ3 + ψ4 is a superposition of two stat ...
BMA 140 B01/B02 Statistical Analysis and Business Decision I
... Statistical data are either reported or interpreted in almost any journal and daily newspaper. Whether as a consumer or a future professional who performs data analysis, today’s world requires you to have a good understanding of the basic concepts of Probability and Statistics. The communication of ...
... Statistical data are either reported or interpreted in almost any journal and daily newspaper. Whether as a consumer or a future professional who performs data analysis, today’s world requires you to have a good understanding of the basic concepts of Probability and Statistics. The communication of ...
Quiz #1
... What is the probability that a respondent owns a GE appliance? Given that a respondent owns a Maytag appliance, what is the probability that the respondent also owns a GE appliance? Are events “M” and “G” mutually exclusive? Why or why not? Explain, using ...
... What is the probability that a respondent owns a GE appliance? Given that a respondent owns a Maytag appliance, what is the probability that the respondent also owns a GE appliance? Are events “M” and “G” mutually exclusive? Why or why not? Explain, using ...
AP Stats Notes
... Decide how accurately you would like to estimate μ. As the number of observations drawn increases, the mean x of the observed values eventually approaches the mean μ of the population as closely as you specified and then stays that close. ...
... Decide how accurately you would like to estimate μ. As the number of observations drawn increases, the mean x of the observed values eventually approaches the mean μ of the population as closely as you specified and then stays that close. ...
Section 3
... There are two traffic lights on the route used by Pikup Andropov to go from home to work. Let E denote the event that Pikup must stop at the first light and F in a similar manner for the second light. Suppose that P(E) = .4 and P(F) = .3 and P(E and F) = .15. What is the probability that he: a) must ...
... There are two traffic lights on the route used by Pikup Andropov to go from home to work. Let E denote the event that Pikup must stop at the first light and F in a similar manner for the second light. Suppose that P(E) = .4 and P(F) = .3 and P(E and F) = .15. What is the probability that he: a) must ...
Lecture 8 1 The Period Finding Problem 2 The Algorithm
... be boosted to be arbitrarily close to 1 by repeating the algorithm several times. (A final note: if we repeat the algorithm several times, we collect several values r1 , . . . , ra such that, with high probability, at least one of them is the correct period. How do we find the correct period out of ...
... be boosted to be arbitrarily close to 1 by repeating the algorithm several times. (A final note: if we repeat the algorithm several times, we collect several values r1 , . . . , ra such that, with high probability, at least one of them is the correct period. How do we find the correct period out of ...
Lec13-BayesNet
... • Use prob tables, in order to set values – E.g. p(B = t) = .001 => create a world with B being true once in a thousand times. – Use value of B and E to set A, then MC and JC ...
... • Use prob tables, in order to set values – E.g. p(B = t) = .001 => create a world with B being true once in a thousand times. – Use value of B and E to set A, then MC and JC ...
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.