Homework Answers
[ARCHIMEDES] Suppose that Xo = 2/3, yo = 3, xn = 2xn-1 Yn-1 xn-1 + Yn-1...
[ARCHIMEDES] Suppose that Xo = 2/3, yo = 3, xn = 2xn-1 Yn-1 xn-1 + Yn-1 and Yn = 1xn Yn-1 for ne N. a) Prove that xnx and Yn 1 y, as n = , for some x, y E R. b) Prove that x = y and 3.14155 < x < 3.14161. (The actual value of x is a.)
What is the period-length of the Linear Congruential Generator Xn+1 = (2Xn + 5)mod13 with seed...
What is the period-length of the Linear Congruential Generator Xn+1 = (2Xn + 5)mod13 with seed Xo = 8? Numeric Answer: ! Cannot be empty What is the period-length of the Linear Congruential Generator Xn+1 = (2Xn + 5)mod13 with seed Xo = 1? Numeric Answer: 1 O Cannot be empty Linear Congruential Generator: Example 2 Homework • Unanswered What is the period-length of the Linear Congruential Generator Xn+1 = (1Xn + 5)mod13 with seed Xo = 1? Numeric Answer:...
2. Let Xn,n0,1,2,... denote a biased random walk given by Xo 0 and Xn+1 Xn + YTHI, where (X } are...
2. Let Xn,n0,1,2,... denote a biased random walk given by Xo 0 and Xn+1 Xn + YTHI, where (X } are 1.1.d. random variables with N(-1,1) distribution. Show that Mn X22n Xn (n -1) is a martingale.
2. Let Xn,n0,1,2,... denote a biased random walk given by Xo 0 and Xn+1 Xn + YTHI, where (X } are 1.1.d. random variables with N(-1,1) distribution. Show that Mn X22n Xn (n -1) is a martingale.
5) Solve each of the following equations. Demonstrate the methods you are supposed to have learned....
5) Solve each of the following equations. Demonstrate the methods you are supposed to have learned. (No credit for guessing answers.) a) (10 pts.) V 4x + 9 – x = 1. 4 20 b) (10 pts.) x-2 = 1 + (x − 2)(x + 3)
Problem 5. A Markov chain Xn, n probability matrix: 0 with states 1, 2, 3 has the following trans...
Problem 5. A Markov chain Xn, n probability matrix: 0 with states 1, 2, 3 has the following transition 0 1/3 2/3 1/2 0 1/2 If P(o-: 1)-P(Xo-2-1/4, calculate E(%) (use a computer).
Problem 5. A Markov chain Xn, n probability matrix: 0 with states 1, 2, 3 has the following transition 0 1/3 2/3 1/2 0 1/2 If P(o-: 1)-P(Xo-2-1/4, calculate E(%) (use a computer).
4. (20 pts) Let {xn} be a Cauchy sequence. Show that a) (5 pts) {xn} is...
4. (20 pts) Let {xn} be a Cauchy sequence. Show that a) (5 pts) {xn} is bounded. Hint: See Lecture 4 notes b) (5 pts) {Jxn} is a Cauchy sequence. Hint: Use the following inequality ||x| - |y|| < |x - y|, for all x, y E R. _ subsequence of {xn} and xn c) (5 pts) If {xnk} is a See Lecture 4 notes. as k - oo, then xn OO as n»oo. Hint: > d) (5 pts) If...
matlab plz Solve the above equation for mi 4 (3 pts Solve following systems of equations...
matlab plz
Solve the above equation for mi 4 (3 pts Solve following systems of equations using 'solver command *+ 2y - Z=1 2x + 3y + z = 2 x + 3y - 2z=1 5) [2 pts] Use fplot to graph the following expression for x values From -3.5 to 2 f(x) = x5 +3.5x* - 2.5x3 + 12.5x2 + 1.5x + 9
If Xo = 3 and Xn = (5xn-1 + 7) mod 200 find x], ..., X...
If Xo = 3 and Xn = (5xn-1 + 7) mod 200 find x], ..., X 10.
(15 pts) 1. For each of the following equations solve for r without using a calculator....
(15 pts) 1. For each of the following equations solve for r without using a calculator. Make sure to show all of your work and give all valid solutions. (a) re3. - .(5e3r) + 6e3r = 0 (b) logg (2 + 6) = 1 - logg (x + 4) (c) log2 (x") = (log, (2)
1. Let k be an integer. Solve the following: (b) ;-164+3 (c) (754-3)(-+1) 2. Solve each...
1. Let k be an integer. Solve the following: (b) ;-164+3 (c) (754-3)(-+1) 2. Solve each of the following equations for : (a) 21 - 5iz = 2zi (b) 49 + 22 = 0 (c) 2 = 2(i-5) (d) := (1 - 2)(1 - 41) (e) : + zi + 12 = 0 3. Solve the linear system of equations: 21 + iz2 = -1 21 - 22 = i 4. Draw plots for the regions described by the following...
[ARCHIMEDES] Suppose that Xo = 2/3, yo = 3, xn = 2xn-1 Yn-1 xn-1 + Yn-1 and Yn = 1xn Yn-1 for ne N. a) Prove that xnx and Yn 1 y, as n = , for some x, y E R. b) Prove that x = y and 3.14155 < x < 3.14161. (The actual value of x is a.)
What is the period-length of the Linear Congruential Generator Xn+1 = (2Xn + 5)mod13 with seed Xo = 8? Numeric Answer: ! Cannot be empty What is the period-length of the Linear Congruential Generator Xn+1 = (2Xn + 5)mod13 with seed Xo = 1? Numeric Answer: 1 O Cannot be empty Linear Congruential Generator: Example 2 Homework • Unanswered What is the period-length of the Linear Congruential Generator Xn+1 = (1Xn + 5)mod13 with seed Xo = 1? Numeric Answer:...
2. Let Xn,n0,1,2,... denote a biased random walk given by Xo 0 and Xn+1 Xn + YTHI, where (X } are 1.1.d. random variables with N(-1,1) distribution. Show that Mn X22n Xn (n -1) is a martingale.
2. Let Xn,n0,1,2,... denote a biased random walk given by Xo 0 and Xn+1 Xn + YTHI, where (X } are 1.1.d. random variables with N(-1,1) distribution. Show that Mn X22n Xn (n -1) is a martingale.
5) Solve each of the following equations. Demonstrate the methods you are supposed to have learned. (No credit for guessing answers.) a) (10 pts.) V 4x + 9 – x = 1. 4 20 b) (10 pts.) x-2 = 1 + (x − 2)(x + 3)
Problem 5. A Markov chain Xn, n probability matrix: 0 with states 1, 2, 3 has the following transition 0 1/3 2/3 1/2 0 1/2 If P(o-: 1)-P(Xo-2-1/4, calculate E(%) (use a computer).
Problem 5. A Markov chain Xn, n probability matrix: 0 with states 1, 2, 3 has the following transition 0 1/3 2/3 1/2 0 1/2 If P(o-: 1)-P(Xo-2-1/4, calculate E(%) (use a computer).
4. (20 pts) Let {xn} be a Cauchy sequence. Show that a) (5 pts) {xn} is bounded. Hint: See Lecture 4 notes b) (5 pts) {Jxn} is a Cauchy sequence. Hint: Use the following inequality ||x| - |y|| < |x - y|, for all x, y E R. _ subsequence of {xn} and xn c) (5 pts) If {xnk} is a See Lecture 4 notes. as k - oo, then xn OO as n»oo. Hint: > d) (5 pts) If...
matlab plz
Solve the above equation for mi 4 (3 pts Solve following systems of equations using 'solver command *+ 2y - Z=1 2x + 3y + z = 2 x + 3y - 2z=1 5) [2 pts] Use fplot to graph the following expression for x values From -3.5 to 2 f(x) = x5 +3.5x* - 2.5x3 + 12.5x2 + 1.5x + 9
If Xo = 3 and Xn = (5xn-1 + 7) mod 200 find x], ..., X 10.
(15 pts) 1. For each of the following equations solve for r without using a calculator. Make sure to show all of your work and give all valid solutions. (a) re3. - .(5e3r) + 6e3r = 0 (b) logg (2 + 6) = 1 - logg (x + 4) (c) log2 (x") = (log, (2)
1. Let k be an integer. Solve the following: (b) ;-164+3 (c) (754-3)(-+1) 2. Solve each of the following equations for : (a) 21 - 5iz = 2zi (b) 49 + 22 = 0 (c) 2 = 2(i-5) (d) := (1 - 2)(1 - 41) (e) : + zi + 12 = 0 3. Solve the linear system of equations: 21 + iz2 = -1 21 - 22 = i 4. Draw plots for the regions described by the following...
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