SkolTech, October 16, 2016
Problems for the mini-course Probability theory
Kabatyansky G.A., Gasnikov A.V. [email protected]
Problem 1 (Random walk, 1.5). There is a point on on one-dimensional integer lattice Z.
With probability 0.5 the point moves t
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\ 9E. X1_XI$Z
x KL 3 6
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WK ix + KL
AM mm A (4;)
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tum-w cfw_WM-L mice
Assignment 2 is made up of the problems taken from [Bertsimas & Tsiliklis, 1997]
Exercise 1.4 costs 2 points. You need to provide a CVX solution.
Exercise 1.8 costs 3 points. You need to write a CVX solution (you can
initialize I* and a to ran
Summary of key matrix and vector algebra definitions and results
Matrices, vectors, transpose
Matrix A of size M N : M rows, N columns.
Matrix elements Aij with i = 1, . . . , M , j = 1, . . . , N , elements can also be written
Problems for the Midterm test
The midterm test will include both theoretical questions and problems based on the material of first 9 lectures.
Note that during the test you are not allowed to use any source of information, e.g. laptop, han
Problem 1 (2 points): as the Skolkovo campus is being built, there is a need to level the hill (the
elevation profile is shown below on the left) to obtain a flat surface with the elevation profile shown
below on the right. Assume that the shape of each t
October 10, 2016
1. Consider an undirected graph G =< V, E > and L = L(G) the Laplacian matrix of the graph G.
Sequence 1 (L) 2 (L) . . . n (L) = 0 is a specturm of the graph G.
upper bound of 1 (L) (such 1 (L) f (|V |, |E|);
Grade 9 Honors Summer Reading
For your honors reading assignment you will read Homer Hickams October Sky and complete
12 journal entries and a character list. We will use these entries and character list as the basis o