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Exercise 1. Two dice are simultaneously rolled. For each pair of events defined below, compute if they are independent or not. (a) A1 ={thesumis7},B1 ={thefirstdielandsa3}. (b) A2 = {the sum is 9}, B2 = {the second die lands a 3}. (c) … Continue reading →

Exercise 1. Suppose that A and B are pairwise disjoint events for which P(A) = 0.3 and P(B) = 0.5.   What is the probability that B occurs but A does not?   What is the probability that neither A nor … Continue reading →

Suppose a License plate must consist of a combination of 8 numbers or letters. How many license plates are there if: there can only be letters?  the first three places are numbers and the last five are letters? the first … Continue reading →

The main educational resource for MA3160 is the following webpage: UConn Undergraduate Probability OER. No book is required and the course will mostly be based on the lecture notes posted here. There will be two midterm exams (in class) and a … Continue reading →

The Department of Mathematics at the University of Connecticut is designating Fall 2018 as a Special Semester in Probability. Special lectures: Srinivasa Varadhan, 9/13 Ofer Zeitouni, 9/20 Elizabeth Meckes, 9/27 Walter Schachermayer, 10/11 Rodrigo Banuelos, 10/18 David Nualart,  10/25 Kavita … 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 →

Practice midterm 1   We will do the correction in class on 09/28.

In the previous lecture we defined the Young’s integral when and with . The integral path has then a bounded -variation. Now, if is a Lipschitz map, then the integral, is only defined when , that is for . With … Continue reading →

Exercise 1. Solve Exercise 44 in Chapter 1 of the book. Exercise 2.  Solve Exercise 3 in Chapter 1 of the book. Exercise 3.  Solve Exercise 39 in Chapter 1 of the book. Exercise 4. The heat kernel on is given by . By … Continue reading →

Exercise 1. The Hermite polynomial of order is defined as Compute . Show that if is a Brownian motion, then the process is a martingale. Show that   Exercise 2. (Probabilistic proof of Liouville theorem) By using martingale methods, prove that if … Continue reading →