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Fluctuation Première S

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So in Mathematics at 1st level S <br> we're not supposed to talk about the notion <br> independence in probability but it is not forbidden to educate <br> students when they speak of the law <br> binomial. Especially if the binomial distribution is introduced <br> with classical Galton board which <br> is already useful to talk concretely coefficients <br> binomial in 1st year level S before extending in the Terminal S <br> Moivre-Laplace theorem. In fact most devices <br> this experimental Galton board, <br> whether real or simulated, pay little attention to two assumptions <br> independence: the first independent <br> successive bifurcations of a ball in <br> his fall. and hypothesis 2: if we ever launched simultaneously a large number of balls, independence between the beads. 2 simulations with 2 sizes of beads <br> show different phenomena bottling and Filmography workaround we have just seen, and, conversely, with balls more <br> small, a phenomenon of liquefaction and Filmography drive which produces an abnormality vis-à-vis this <br> as predicted by theory, here you will get carried away by the momentum of <br> fluid is going to say, two vertices on the ends rather <br> at the center. So to really talk about law <br> binomial with a Galton board and Filmography So seriously talk of independence, successive rebounds on rows <br> nails, it is welcome that make a <br> simulation. So what it gives here? If I <br> not going too fast, first drop gives 3 rebounds <br> a second straight 4 gives a <br> third gives 7 and therefore as and when it appears as <br> in the table in the diagram <br> right in Figure 2, experimental frequencies <br> successive should gradually closer asymptotically our theoretical probabilities. I get tired of it, so I'll <br> increase speed, I reset and then rather do <br> fall 100 100 logs, although of course we do this <br> plus chuttes, 100 by 100 and then maybe support 20 <br> time for 2000 2000 beads falling ... Obtain frequencies and therefore beginning to adjust to the <br> theoretical probabilities. So it allows us to speak of <br> intervals fluctuation which <br> way? As follows ... I open a new window. <br> Then under the Insert Text tool, there is a <br> interesting module Probability Calculations we are the first S so we <br> speak as the binomial distribution, Here we had earlier 10 rows. <br> Then we will arrange a little more room <br> for our business. What is very interesting is that we <br> can speak of the distribution function <br> like that, with the "left" tab, simply a value from 0 to I <br> gives in this field, say 7 or with <br> the tab is here And so the question for <br> determine the range of fluctuation in <br> confidence level 95% half the risk of saying something stupid that <br> would be 2.5% underperformance and presto, that we <br> immediately gives k1 = 2 See that it took the value <br> immediately above 2.5%, or <br> probability the next higher value <br> 0,025 And on the other side, then, for <br> outperformance could say, you hit .975 in this field and it will <br> fit the value immediately <br> top, and a k2 k1 = 2 and k2 = 8 So obviously, with very little <br> rows of nails, it is not very <br> impressive, but the processing speed is very precious <br> when compared to that of calculators There, like, I want to know if I put k1 <br> 0025 and I get 40, and if I want to know k2, I put 0975, and I get k2 = 60. So obviously, with probability p = 1/2, there is a <br> symmetry but if the symmetry is broken putting, for example, p = pi / 4, <br> same case, k1 is equal to 70 <br> and Filmography k2 is equal to 86. Then the a priori risk has no reason <br> to be set once for all 5% this can be a risk in various <br> concrete situations largest to smallest, it would give <br> various fluctuation intervals, but in the first program S one remains in this interval fluctuation <br> 5%.

Video Details

Duration: 5 minutes and 13 seconds
Country: France
Language: French (France)
Producer: mathsinfo
Director: mathsinfo
Views: 20
Posted by: reivilosenior on May 25, 2014

Intervalle de fluctuation au seuil de confiance 95% en Première S: une présentation possible via une simulation de la planche de Galton

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