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[18:14:15] *** Roman добавил Maxim Timonin, Юля к этому чату *** [18:14:17] *** Групповой звонок *** [18:19:26] Roman: макс [18:24:35] Roman: 3^(3^100000) > 4^(2^100000) [18:24:41] Roman: log(2^1000)(3^100) < log(3^10000)(2^1000) [18:24:58] Roman: None of the above [18:26:29] Roman: We have a function F defined as: F(x) = 11 * x What is the value of the ratio defined as the variance of F(x) divided by the variance of x? [18:28:30] Roman: For any integer k > 2, which equation below depicts exponential decay? [18:28:43] *** Roman добавил Сергей Шохарев к этому чату *** [18:30:32] Roman: Two points are chosen, uniformly and independently distributed, on a line of length 60. What is average (expected) distance between them? [18:33:15] Roman: If |a - M| <= c, and |b - M| <= d, which of the following statements is sufficient to imply that |a - b| < e? [18:33:36] Roman: A. |c - d| < e B. |c - d| <= e [18:33:56] Roman: С. c + d < e Either d < c + e or c < d + e [18:35:15] Roman: There are three containers of pens. One container has red pens, one has blue pens, and one contains both red and blue pens. Each container is labeled. One is labeled "red", one "blue", and one "red and blue". However, none of the containers' labels match the contents, and you want to fix this. If you are only allowed to sample just one pen from just one of the containers, what would you do so you can fix the labels on the containers? A. Sample a pen from the container labeled "red" B. Sample a pen from the container labeled "red and blue" C. Sample a pen from the container labeled "blue" D. Sample a pen from any of the three containers E. None of the above is sufficient [18:38:18] Roman: When flipped, a biased coin has a probability of 0.9 for heads. If you get $1 for heads and lose $10 for tails, what is your expected wealth after 10 tosses? A. One cannot know from the given information. B. Expected wealth < 0 C. Expected wealth = 0 D. Expected wealth > 0 [18:40:23] Roman: Below is a list of asymptotic complexities of eight functions, each with input of length N: A. O(N^3) B. O(Log(n)) C. O(Sqrt(n)) D. O(N * log(n)) E. O(2^N) F. O(N^N) G. O(N!) H. O(Log(Log(n))) Sort the functions by order of growth, with slower-growing functions first. Your solution should be a sequence of letters corresponding to the functions above. For example, "BACFDEHG". [18:41:02] Roman: Below is a list of asymptotic complexities of eight functions, each with input of length N: A. O(N^3) B. O(Log(N ) ) C. O(Sqrt(N ) ) D. O(N * log(N ) ) E. O(2^N ) F. O(N^N ) G. O(N!) H. O(Log(Log(n) ) ) Sort the functions by order of growth, with slower-growing functions first. Your solution should be a sequence of letters corresponding to the functions above. For example, "BACFDEHG". [18:42:45] Roman: E. O(2^N ) F. O(N^N ) G. O(N ! ) H. O(Log(Log(N ) ) ) [18:44:07] Roman: 9 0,4 1,43 0,47 [18:44:20] Maxim Timonin: 8 27 6 [18:44:29] Roman: The population of a desolate, remote planet is kept alive by a life support system. The population quadruples every 54 years, but the life support system's capacity can only be doubled every 54 years. If the initial population is 2 people, and the initial life support system has capacity for 16384 people, in how many years will the population outgrow the life support system? [18:48:34] Roman: Given the following program, what is the final value of C? A is equal to 167 B is 91 C is 0 While A-2 is strictly greater than B Subtract two from A And add one to C [18:52:16] Roman: ответ 37 [18:52:30] Roman: You need to forecast a number that will be drawn from a continuous uniform distribution between 0 and 60. You will be charged 3 dollars for every unit you overestimate (so if the number is 10 and you say 12, then you will be charged 2 * 3 = 6 dollars), and you will be charged 1 dollar for every unit you underestimate. If you forecast correctly, then you will not be charged at all. What number should you forecast to minimize your expected cost? [18:56:36] Roman: In a sequence of fair coin tosses, what is the probability P of getting HHH before THH? A. 0 < P < 0.08 B. 0.08 < P < 0.11 C. 0.11 < P < 0.14 D. 0.14 < P < 0.2 E. 0.2 < P < 1 [19:00:39] Roman: Assume that one can flip a fair coin once every second and will do so for 100 years without stopping. True or false: one will not observe a sequence of 100 consecutive heads with 99.99% probability. A. True B. False C. Not enough information to decide [19:05:38] Roman: Let P(n,m) be a property about two integers n and m. If we want to DISPROVE the claim, "There exists an integer n such that P(n,m) is true for all integers m", then we need to prove that: A. There exists an integer m such that P(n,m) is false for all integers n. B. If P(n,m) is true, then n and m are not integers. C. For every integer n, and every integer m, the property P(n,m) is false. D. For every integer n, there exists an integer m such that P(n,m) is false. [19:08:37] Roman: What is the value of the variable sum after the following pseudo-code runs? sum = 0 for n in range 1 to 100 (inclusively): if n is odd: sum = sum + n else: sum = sum - 2 [19:11:23] Roman: 2400 [19:11:33] Roman: What is the maximal possible variance of a random variable taking values in the interval [0, 10]? [19:13:42] Roman: A stock's price fluctuates every day by going up exactly 5% or going down exactly 5%. Assume that each direction is equally likely. Assume zero trading costs, zero interest rate, and no dividends. What strategy is most likely to be profitable after 100 days? A. Buying or selling will produce the same result. B. Cannot know from the given information. C. Buy the stock. D. Sell the stock. [19:16:43] Roman: A vector X of 100 real numbers has a mean value of 14. A second vector Y of 100 real numbers has a mean value of 40. A third vector Z is constructed by picking 100 numbers from X or Y at random and multiplying each by 2. A fourth vector W is constructed by picking the remaining 100 numbers of X and Y and multiplying each by 2. What is the sum of all elements in Z + W? [19:18:49] Roman: What is the value of the variable A after running the following program? A = 0 B = 2 While (B < 30) If (B is a prime number) A = A + 81 End B = B + 1 End [19:21:34] Roman: Initially, there are 500 kilograms of tomatoes. By mass, the tomatoes are 99% liquid and 1% solid. Then, some liquid evaporates, and the tomatoes are now 98% liquid and 2% solid. How many kilograms evaporated? A. 120 B. 250 C. 260 D. 130 E. 230 [19:23:50] Roman: This section will contain 20 questions. Once you started, you will need to finish each question within the time limit. If you are ready to proceed, click "Continue". If you don't have time to finish all the questions at this moment, you can close the browser and login again when you have time to start this section. [19:24:54] *** Звонок завершен. Продолжительность: 1:10:37 *** [19:25:02] Roman: В 19.40 [19:35:16] *** Групповой звонок *** [19:39:30] *** Групповой звонок *** [19:41:51] Roman: Consider a polynomial f(x) and its derivative f'(x) that are related according to: f(x) - f'(x) = x^3 + 3*x^2 + 3*x + 1 What is f(9)? [19:48:03] Maxim Timonin: 9*f = 1000 [19:49:41] Сергей Шохарев: 1366 [19:49:56] Roman: Given the following 3x3 matrix A: 1 2 2 2 2 1 1 2 1 What is the determinant of the inverse of A? [19:51:31] Maxim Timonin: Matrix(3, 3, {(1, 1) = 0, (1, 2) = 1, (1, 3) = -1, (2, 1) = -1/2, (2, 2) = -1/2, (2, 3) = 3/2, (3, 1) = 1, (3, 2) = 0, (3, 3) = -1}) [19:51:50] Roman: http://otvet.mail.ru/question/3229744 [19:51:50] Maxim Timonin: 1/2 [19:54:03] Roman: here are ten islands in a line. Between each pair of consecutive islands, there are two bridges, one strong and one weak. (There are no bridges between non-consecutive islands.) There is no way to tell if a bridge is strong or weak except to walk over it. A strong bridge allows you to cross safely. A weak bridge immediately breaks and disappears when walked on, and you fall into the water and are carried back to the first island. You are situated on the first island and want to get to the tenth island. What is the expected number of strong bridges you will cross en route to the tenth island? [20:00:03] Roman: Seven people are in an argument, but potentially some or all of them are liars. They give the following statements: Bob: "No one lies." Jennifer: "No one tells the truth." Conrad: "Jennifer is not a liar." Tom: "Conrad and Sherry always lie at the same time." Sherry: "Danny never lies." Danny: "Sherry is a liar." Adam: "Danny sometimes lies." How many of them are lying? [20:07:09] Roman: What is the minimal natural number that ends with digit 4 such that moving its last digit to the first position (i.e. 1234 => 4123) increases it exactly fourfold? [20:11:14] Roman: There are 4 green and 60 red apples in a basket. They are removed one-by-one, without replacement, until all 4 green ones are extracted. What is the expected number of apples that will be left in the basket? [20:16:18] Roman: Given two assets that have expected excess returns of 7 and 4, and given their expected covariance matrix: 2 1 1 1 What is the maximum expected Sharpe ratio that you can achieve by combining the two assets into a portfolio? [20:25:16] Roman: Three riflemen A, B, and C take turns shooting at a target. The first rifleman to hit the target gets 2002 dollars. A shoots first, B second, and C third, after which the cycle repeats again with A, until one of the riflemen hits the target. Each hits the target with probability 0.5. What is rifleman A's expected winnings in dollars? [20:32:48] Roman: WorldQuant Recruitment Exam Triangle ABC has sides of length 45, 60, and 75. Place a point D randomly and uniformly inside the triangle. What is the expected value of the sum of perpendicular distances from point D to the triangle's three sides? [20:39:27] Roman: What will be the value of C after running the following pseudo-code? A is 1 B is 100 C is 0 Loop 10000 times: C is average of A and B If A is equal to C or B is equal to C: Exit Loop Set A to B Set B to C A. Between 0 and 35 B. Between 35 and 45 C. Between 45 and 55 D. Between 55 and 65 E. Between 65 and 75 F. Between 75 and 100 [20:44:32] Roman: How many times a day do the hour and minute hands of an analog clock form a right angle? [20:48:10] Roman: There is a unit cube with internal mirror faces. A ray is emitted into the cube from one vertex, reflects off four faces (without touching vertices or edges), and stops at the opposite vertex from which it started. What is the minimum possible distance the ray travels? The answer should be decimal format approximated to 4 digits of precision, i.e. format a.bcd as in 1.234. [20:53:16] Roman: Given the following function definition: define f(x): result = 1 for i from 1 to x (inclusively): result = result + i return result How many additions will take place while evaluating f(f(f(3)))? [20:58:18] Roman: A pedestrian starts walking from town A to town B. At the same time, another pedestrian starts walking from town B to town A. They pass each other at noon and continue on their paths. One of them arrives at 4 PM, the other at 9 PM. How many hours had each walked before passing each other? [21:04:23] Roman: You have a function F that computes the product of matrices. If X is MxN matrix and Y is NxK matrix then F(X,Y) is going to output matrix product X*Y and take MxNxK nanoseconds. You need to calculate a product of five matrices, P = A * B * C * D * E. The dimensions of the matrices are as follows: A is 2x100, B is 100x10, C is 10x10, D is 10x100, and E is 100x2. How many nanoseconds does it take to calculate P in the fastest way possible using only function F? [21:10:31] Roman: The three distinct entries of a 2 x 2 symmetric matrix are drawn from the uniform distribution [-60, 60]. What is the expected determinant of the matrix? Answer: [21:16:35] Roman: If WHITE=000, RED=101, BLUE=110, and PURPLE=100, then what three-digit string corresponds to YELLOW? Answer [21:20:38] Roman: What are the last 4 digits of 2015^(2013^2014)? (Here ^ denotes exponentiation, for example 2^3 = 8.) [21:26:47] Roman: Nine boys and seven girls are seated randomly around a circular table with 16 seats. Find the expected number of girl-boy neighbors. For example, in the seating below there are four such pairs. GBBBBB G B G B GGGBBG [21:33:54] Roman: A city is composed of three parallel east-west streets and four parallel north-south streets: _ _ _ |_|_|_| |_|_|_| Note there are 12 intersections and 17 street segments. A policeman needs to visit every street segment, but he wants to take the shortest path. The policeman can start at any intersection, and he can only traverse streets, going from one intersection to another. How many street segments are there in the shortest path that visits each street segment at least once? [21:41:18] Roman: Your results have been submitted. You will be contacted if there is further interest. Thank you for your time.
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