Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 9.1, Problem 5E
To determine
To show:Using given LCG the
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A company that operated 10 hours a daymanufactures two products on threesequential processes. The following tablesummarizes the data for the problem:
Suppose that a single binary digit (0 or 1) is to be transmitted through a transmission
channel. Because of the noise in the channel, the received binary digit can be in error. A schematic
of a probabilistic model for this situation is shown in the figure below, for which
P[X=0]=q,
P[X=1] =p=1-q₂
and
P[Y=0/X=0]=Po
P[Y=1/X=0] =q=1 - Po
P[ Y = 0/ X = 1 ] =q₁ = 1- P₁
P[Y=1/X=1] = P₁
where X is the transmitted digit and Y is the received digit.
a) Determine the probability that the digit 1 is received.
b) Determine the probability that an error occurs, given that the digit 1 was transmitted.
c) Determine the unconditional probability of error.
3.7 Nikita creates an RSA cryptosystem with public key
(n, e) = (1433811615146881, 329222149569169).
In the following two problems, show the steps you take to factor n.
(Don't simply factor n directly using a computer.)
(a) Somehow you discover that d = 116439879930113. Show how to
use the probabilistic algorithm of Section 3.4.3 to factor n.
(b) In part (a) you found that the factors p and q of n are very
close. Show how to use the Fermat Factorization Method of Sec-
tion 3.4.2 to factor n.
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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