Math 213
Exam 1 (Solutions) February 22, 2008
Prof. I.Kapovich
Problem 1[20 points] For each of the following statements indicate whether it is true or false. You do not have to explain your answers. (1) For the set S = cfw_, cfw_, cfw_ we have |S | = 1.
Math 213
Exam 2 (Solutions)
Prof. I.Kapovich April 10, 2007 Problem 1 A binary string x of length 20 is chosen at random. Let X be the random variable where X (x) is the number of 0s in x plus twice the number of 1s in x. Find E (X ) and V (X ). Solution.
Math 213, Section B1, Quiz 1 (Solutions); Friday, Jan 26, 2007 1. Let A = cfw_, cfw_, 1, 2, cfw_, B = cfw_1, 2, 3 and C = cfw_1, . (1) Find |A|, |B | and |C |. (2) Find the sets A B and A C . (3) Is it true that C A? (4) Is it true that A A? (5) Is it tru
Math 213, Section B1, Quiz 2 (SOLUTIONS); Friday, February 2, 2007 1. Using induction, prove that for every integer n 2 3n 2n2 + 1. Solution. 1) Base of Induction. First, check if the statement 3n 2n2 + 1 holds for n = 2. We have 32 = 9 and 2 22 + 1 = 2 4
Math 213, Section B1, Quiz 3 (Solutions); Friday, February 9, 2007 1. For a standard 52-card deck nd the number of all 4-card hands that contain exactly one ace. Give the details of your work. Solution. There are 4 aces and 48 non-ace cards in a 52-card d
Math 213, Quiz 6 (Solutions); Friday, February 29, 2008 1. Let n 2 be an integer. A bit-string of length n is chosen at random. Let X = 3j where j is the number of 1-bits in the string chosen. Find EX and V X . Provide a detailed explanation of your answe
Math 213, Section B1, Quiz 8 (SOLUTIONS); Friday, March 30, 2007 1. How many ways are there to distribute 5 dierent toys among 3 dierent children if every child must get at least one toy? Solution. We have to count the number of onto functions from a 5-el