Author Archives: Fabrice Baudoin

This is a talk about sub-Laplacian comparison theorems on Sasakian manifolds given   at the Institut Fourier in Grenoble in October 2018. The associated paper, written in collaboration with Erlend Grong, Kazumasa Kuwada and Anton Thalmaier can be downloaded here. … 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 15% 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(1−x) 0≤x≤1, 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 →

  Exercise 1. Rachel receives  an average of two texts every 3 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 →

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 →

Exercise 1. Two dice are rolled. Consider the events A = {sum of two dice equals 3}, B = {sum of two dice equals 7 }, and C = {at least one of the dice shows a 1}. (a) What … Continue reading →