Author Archives: Fabrice Baudoin

HW9. MA3160 Fall 2017

Exercise. Let X, Y have joint density if and 0 otherwise. (a)  Find c that makes this a joint pdf: (b) Find P (X < Y ).  

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HW8. MA3160 Fall 2017

Exercise 1.  About 10% of the population is left-handed. Use the normal distribution to approximate the probability that in a class of 150 students, (a) at least 25 of them are left-handed. (b) between 15 and 20 are left-handed.   … Continue reading

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HW7. MA3160 Fall 2017

Let X be a random variable with probability density function: f(x) =cx(5−x) 0≤x≤5, 0 otherwise. (a) What is the value of c? (b) What is the cumulative distribution function of X ? That is, find F (x) = P (X … Continue reading

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Lecture 8. Rough paths Fall 2017

In this lecture, it is now time to harvest the fruits of the two previous lectures. This will allow us to finally define the notion of -rough path and to construct the signature of such path. A first result which … Continue reading

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HW6. MA3160 Fall 2017

  Exercise 1. Patricia receives  an average of two texts every 2 hours. If we assume that the number of texts is Poisson distributed, what is the probability that she receives five or more texts in a 9 hours period? Exercise … Continue reading

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HW5. MA3160 Fall 2017

Exercise 1. Three balls are randomly chosen with replacement from an urn containing 5 blue, 4 red, and 2 yellow balls. Let X denote the number of red balls chosen. (a) What are the possible values of X? (b) What … Continue reading

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Annales de la faculte des sciences de Toulouse

Annales de la Faculte des Sciences de Toulouse is a peer-reviewed international  journal with a long tradition of excellence (going back to 1887 and Thomas Stieltjes). The journal periodically publishes surveys by the recipients of the Fermat Prize.  The Editorial Board encourages … Continue reading

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