Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 9.2, Problem 4CP
To determine
To solve: For given
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3.) Johns Hopkins reports two numbers daily for all the US states:
P(t): the total number of cases confirmed on day t or before
N(t): number of new cases reported on day t
a.) What is P(t+1)-P(t) in terms of N?
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3
Chapter 9 Solutions
Numerical Analysis
Ch. 9.1 - Find the period of the linear congruential...Ch. 9.1 - Find the period of the LCG defined by a=4,b=0,m=9...Ch. 9.1 - Approximate the area under the curve y=x2 for 0x1,...Ch. 9.1 - Approximate the area under the curve y=1x for 0x1,...Ch. 9.1 - Prob. 5ECh. 9.1 - Prove that u1=x21+x22 in the Box-Muller Rejection...Ch. 9.1 - Implement the Minimal Standard random number...Ch. 9.1 - Implement randu and find the Monte Carlo...Ch. 9.1 - (a) Using calculus, find the area bounded by the...Ch. 9.1 - Carry out the steps of Computer Problem 3 for the...
Ch. 9.1 - Use n=104 pseudo-random points to estimate the...Ch. 9.1 - Use n=104 pseudo-random points to estimate the...Ch. 9.1 - (a) Use calculus to evaluate the integral 01x2x,...Ch. 9.1 - Prob. 8CPCh. 9.1 - Prob. 9CPCh. 9.1 - Devise a Monte Carlo approximation problem that...Ch. 9.2 - Prob. 1CPCh. 9.2 - Prob. 2CPCh. 9.2 - Prob. 3CPCh. 9.2 - Prob. 4CPCh. 9.2 - Prob. 5CPCh. 9.2 - One of the best-known Monte Carlo problems is the...Ch. 9.2 - Prob. 7CPCh. 9.2 - Prob. 8CPCh. 9.2 - Prob. 9CPCh. 9.3 - Design a Monte Carlo simulation to estimate the...Ch. 9.3 - Calculate the mean escape time for the random...Ch. 9.3 - In a biased random walk, the probability of going...Ch. 9.3 - Prob. 4CPCh. 9.3 - Design a Monte Carlo simulation to estimate the...Ch. 9.3 - Calculate the mean escape time for Brownian motion...Ch. 9.3 - Prob. 7CPCh. 9.4 - Use Itos formula to show that the solutions of the...Ch. 9.4 - Use Itos formula to show that the solutions of the...Ch. 9.4 - Use Itos formula to show that the solutions of the...Ch. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.4 - Prob. 6ECh. 9.4 - Use the Euler-Maruyama Method to find approximate...Ch. 9.4 - Use the Euler-Maruyama Method to find approximate...Ch. 9.4 - Apply the Euler-Maruyama Method with step size...Ch. 9.4 - Prob. 4CPCh. 9.4 - Prob. 5CPCh. 9.4 - Prob. 6CPCh. 9.4 - Use the Milstein Method to find approximate...Ch. 9.4 - Prob. 8CPCh. 9.4 - Prob. 9CPCh. 9.4 - Prob. 10CPCh. 9.4 - Prob. 11CPCh. 9.4 - Prob. 12CPCh. 9.4 - Prob. 1SACh. 9.4 - Prob. 2SACh. 9.4 - Prob. 3SACh. 9.4 - Prob. 4SACh. 9.4 - Compare your approximation in step 4 with the...Ch. 9.4 - Prob. 6SA
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- 2. Each of 12 refrigerators of a certain type has been returned to a distributor because of the presence of a high-pitched oscillating noise when the refrigerator is running. Suppose that four of these 12 have defective compressors and the other eight have less serious problems. If they are examined in random order, let ? be the number among the first six examined that have a defective compressor. Compute (a) ?(? = 1), (b) ?(? ≥ 4), and (c) ?(1 ≤ ? ≤ 3).arrow_forward4arrow_forwardI roll a die with 10 faces numbered 0-9 and obtain a score X. What is E(X)? In order to obtain a random number between 0 and 99 I roll the die twice obtaining scores X and Y, then set Z = 10X + Y (i.e., the first roll determines the "tens", the second roll the "ones"). Is it true to say that E(Z) = 10E(X) + E(Y)?arrow_forward
- 1) Consider a memoryless discrete-time source which emits a sequence of random elements X1, X2, · where xk for each integer k can be any of a1, a2, az and a4. Assume ... that Prob(xk a1) = 0.01, Prob(xk a2) 0.1 and Prob(xk аз) = 0.3. Answer the following questions: b) What is the (simplest) relationship between the entropy of xk and the entropy of (Xk, Xk+1)?arrow_forward2: Find: 1 [²¹(3) S3arrow_forward2.2.4 Augustus de Morgan satisfied his own problem: I turn(ed) x years of in the year x. (a) Given that de Morgan died in 1871, and that he wasn't the beneficiary of some miraculous anti-aging treatment, find the year in which he was born. (b) Suppose you have an acquaintance who satisfies the same problem. How old will they turn this year? Give a formal argument which justifies that you are correct.arrow_forward
- 1) Consider a memoryless discrete-time source which emits a sequence of random elements X1, X2, ,Xk,··, where xk for each integer k can be any of a1, a2, a3 and a4. Assume •', that Prob(xk = a1) = 0.01, Prob(Xk = a2) 0.1 and Prob(xk a3) = 0.3. Answer the following questions: d) For each fixed integer l, we can apply Huffman's method to encode average realization of (Tnl+1, Xnl+2, · ·· , Xnl+n) where n is another integer. The average codeword length of the resulting codebook is denoted by Ln. What is the limit of Ln/n as n → 0? Is this codebook for xnl+1, Xnl+2, , X'nl+n dependent on l? Why?arrow_forwardConsider the following model to grow simple networks. At time t = 1 we start with a complete network with no = 6 nodes. At each time step t> 1 a new node is added to the network. The node arrives together with m = 2 new links, which are connected to m = 2 different nodes already present in the network. The probability II, that a new link is connected to node i is: N(t-1) II₁ = ki - 1 Z == with Z = (k; -1) j=1 where k; is the degree of node i, and N(t - 1) is the number of nodes in the network at timet - 1. (e) Write down the master equation of the model, i.e. the equation that describes the evolution of the average number N(t) of nodes that at time t have degree k.arrow_forwardConsider the following model to grow simple networks. At time t = 1 we start with a complete network with no = 6 nodes. At each time step t> 1 a new node is added to the network. The node arrives together with m = = 2 new links, which are connected to 2 different nodes already present in the network. The probability II; that a new link is connected to node i is: m = N(t-1) Π ki - 1 Z with Z = Σ (ky - 1) j=1 I where ki is the degree of node i, and N(t - 1) is the number of nodes in the network at time t-1.arrow_forward
- . A research center claims that at least 23% of adults in a certain country think that their taxes will be audited. In a random sample of 900 adults in that country in a recent year, 19% say they are concerned that their taxes will be audited. At α=0.01, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha.arrow_forwardEach of 14 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 9 of these refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 6 examined that have a defective compressor. (I have figured out part "a" but need help with "b" and P(X ≤ 3) in "c") (a) Calculate P(X = 4) and P(X ≤ 4). (Round your answers to four decimal places.) P(X = 4) = P(X ≤ 4) = (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) (c) Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 25 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately)…arrow_forwardIf Ô₁ and ₂ are unbiased estimators of the same parameter 0, what condition must be imposed on the con- stants k₁ and k2 so that k₁ Ô₁+k₂Ô₂ is also an unbiased estimator of 0?arrow_forward
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