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Suppose n activities apply for using a common resource. Activity ai (1 ≤ i ≤ n) has a starting time S[i] and a finish time F[i] such that 0 < S[i] < F[i]. Two activities ai and aj (1 ≤ i, j ≤ n) are compatible if intervals [S[i], F[i]) and [S[j], F[j]) do not overlap. We assume the activities have been sorted such that S [1] ≤ S [2] ≤ …≤ S[n]. (a) Design an O(n2) dynamic programming algorithm...
Question 6: Let n 2 2 be an integer and let ai,a2,...,an be a permutation of the set (1, 2, . . . ,n). Define ao = 0 and an+1 = 0, and consider the sequence do, 1, d2, l3, . . . , Un, Un+1 A position i with 1 i n is called auesome, if ai > ai-1 and ai > ai+1. In words, i is awesome if the value at position i is larger than both its...
1) Show that for every 1 Sisn, P(AA)>o 2) Show that PA, n nA")-P(AJPA,İA, )PA,İA, n As) P(A"IA, n nA"-.). Remark. This identity is called the compound probability theorem and is for instance useful in situations where the pašt has an influence on the future (and is in some sense the probabilistic version of the "multiplicative rule") 3) (Application) Consider an urn with 6 identical blue balls and 4 identical red balls. Take one after the other 3 balls at...
QUESTION 6 (2 pts). Exercise 2.3.2 Suppose A є Mn,n(F) and that λ is an eigenvalue of A. Show that, for any choice of vector norm on Fn, we have lAll-A, where |All is the associated matrix norm of A. QUESTION 6 (2 pts). Exercise 2.3.2 Suppose A є Mn,n(F) and that λ is an eigenvalue of A. Show that, for any choice of vector norm on Fn, we have lAll-A, where |All is the associated matrix norm of A.
Problem 2. Let n be a positive integer. We sample n numbers ai,...,an from the set 1, 2,...,n} uniformly at random, with replacement. Say that the picks i and j with i < j are a match if a -aj. What is the expected total number of matches? Hint: Use indicators. Wİ
replace ai with Ki if konu K, 16 for i 22 ai-ai-l tai-2 prove that ulan for no using Starp induction
A random number N of dice is thrown. Let Ai be the event that N = 1, and assume that P(A) 2-1i 2 1. The sum of the scores is S. Find the probability that: (a) N- 2 given S-4; (b) N 2 given that S 4 and the first die showed 1
6. Gently couple ale po ial accounting manuale choch ia and managerial accounting financial norm a l accounting 2. Which of the following is not a user or financial reports Chador Covernment ancies Employees 3. The financial statements most frequently provided include all of the following except the balance sheet income statement statement of cash flows. d. statement of retained earnings 4 The information provided by financial reporting pertains to a individual business enterprises, rather than to industries or an...
2. For each p> 1, denote by || . || the norm in R" defined by: n || 2 || p = [f(x)}; where f(x) = 5:), Vx = ((1, ... , In) € R". i=1 For p > 1 and r* in the dual of R", consider the following optimization problem: n(x*) = sup|(2*, 2) : ||- ||| < 1] = sup[(x*, r) : f(x) < 1] 1 . Prove that n(x*) = || 2* ||g, where q> 1...
How do you do this Linear Algebra problem? 6. Let A [ai i be an mxn matrix with RREF R-FF. Prove that i.. Tn there exists an m × m invertible matrix E such that аґ Eri for 1-i-n 6. Let A [ai i be an mxn matrix with RREF R-FF. Prove that i.. Tn there exists an m × m invertible matrix E such that аґ Eri for 1-i-n