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Author Archives: Fabrice Baudoin
From January 15th to January 30th, I will have the great pleasure to visit the TIFR Centre For Applicable Mathematics in Bangalore, India. I will be lecturing on some aspects of geometric inequalities on sub-Riemannian manifolds. Here is a preliminary version … Continue reading
Exercise. Let X, Y have joint density if and 0 otherwise. (a) Find c that makes this a joint pdf: (b) Find E (X Y^2 ). (c) Find Var(X+Y)
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 ).
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
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
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