Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 9.3, Problem 6CP
Calculate the mean escape time for Brownian motion for the intervals in Computer Problem 5. Carry out
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3) Fresh tomatoes were stored at 15°C. Lycopene (orange-red pigment) contents were
determined for a period of 10 weeks at 15°C. The results are presented in Table 3.
Lycopene degradation during storage of tomatoes is known to give the straight line in a
semi-log graphic paper.
Table 3– Lycopene contents in fresh tomatoes stored at 15°C
Storage time
(week)
Lycopene content
(mg/kg)
33
2
23
6
5.3
10
2.1
Find out the lycopene concentration in tomatoes after 4 months of storage at 15°C.
Note: Give units wherever it is applicable!!!!
Σxy- (Σx Σy / )
ΣyΣx?- Σx Σxy
Ex² - [ (Ex)² / n) ]
n (E x² - [ (Ex)² / n) ] )
Jitter is a term used to describe the variation in conduction time of a water power system. Low
throughput jitter is eritical to successful waterline technology. An investigation of throughput
jitter in the opening switch of a prototype system yielded the following descriptive statistics on
conduction time for 18 trials: =334.8 nanoseconds and s = 6.3 nanoseconds. (Conduction time
is defined as the length of time required for the downstream current to equal 10% of the
upstream current.)
a) Construct a 95% confidence interval for the true standard deviation of conduction times
of the prototype system.
b) A system is considered to have low throughput jitter if the true standard deviation of
conduction times is less than 7 nanoseconds. Does the prototype system satisfy this
requirement? Use a = 0.01.
If the population of an ant colony in 5 days is known to be 1100 and P'(0)=3 , what is the approximate current population of the ant colony? Assume the population grows linearly
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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