
Matlab, Fourth Edition: A Practical Introduction to Programming and Problem Solving
4th Edition
ISBN: 9780128045251
Author: Stormy Attaway Ph.D. Boston University
Publisher: Elsevier Science
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Chapter 12, Problem 12.2P
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b. 2 (4 points). We consider the problem:
y' (t) = |y(t)|³ .
(1)
(1) (2 points). Suppose y(t) is a solution to (1), show that the graph of y is either
entirely in the upper open plane {(t, y) y > 0}, or entirely in the lower open
:
plane {(t, y) : y 0, y = 0, and y < 0.)
ob. 3 (4 points). Let us consider the equation:
v'
= -ευ - 9,
v(0) = 0,
where g > 0 and ε are constants.
Let the solution be denoted v(t, ε), we use two different methods to show that v depends
continuously on ɛ.
(1) (2 points). Defining y₁(t) = v(t) and y2(t) = ε, they solve the IVP:
d [y1(t)
dt
[v1(t)] =
[f1(y1, y2)] def
[f2 (Y1, y2)]
-Y1Y2 — g]
0
[31(0)
=
[
,
show that fi is local Lipschitz in (⁄1, Y2). That is, for all (y1, y2) Є R², we can
find constants a, b, L > 0 such that for all (x1, x2), (Z1, Z2) Є [y1 − a, Y1 + a] × [Y2 −
b, y2b], we have |f1(x1, x2) — f1(21, 22)| ≤ L max(|x1 — 21|, |x2 − 22|).
-
-
(2) (2 points). Find v(t, ε) explicitly and show that v(t, ɛ) = C(R², R).
Background: Data on infant mortality (measured as deaths per 1,000 under 1 year old) was collected by
the United Nations Educational, Scientific, and Cultural Organization (UNESCO) for the 1990 Demographic
Year Book and is provided below. Perform an analysis of variance procedure to determine whether or not
the differences in the mortality rates of infants in African, Asian and Middle Eastern countries is
statistically significant.
Directions: Perform an analysis of variance (ANOVA) to determine if the differences in the infant mortality
rates in African, Asian and Middle Eastern countries is statistically significant.
1. Click on the Data button below to display the data. Copy the data into a statistical software package
and click the Data button a second time to hide it.
Click this button to reveal the data. Click again to collapse it.
Africa
Asia
MiddleEast
69 180.6
16
137
120
108.1
64
129
70
69
32
11.7
45.4
6.1
44
140
91
15.6
103
75
47
143
26
42
88
25
71
68
69
75
79
127
26
128…
Chapter 12 Solutions
Matlab, Fourth Edition: A Practical Introduction to Programming and Problem Solving
Chapter 12, Problem 12.1PChapter 12, Problem 12.2PChapter 12, Problem 1EChapter 12, Problem 2EChapter 12, Problem 3EChapter 12, Problem 4EChapter 12, Problem 5EChapter 12, Problem 6EChapter 12, Problem 7EChapter 12, Problem 8E
Chapter 12, Problem 9EChapter 12, Problem 10EChapter 12, Problem 11EChapter 12, Problem 12EChapter 12, Problem 13EChapter 12, Problem 14EChapter 12, Problem 15EChapter 12, Problem 16EChapter 12, Problem 17EChapter 12, Problem 18EChapter 12, Problem 19EChapter 12, Problem 20EChapter 12, Problem 21EChapter 12, Problem 22EChapter 12, Problem 23EChapter 12, Problem 24EChapter 12, Problem 25EChapter 12, Problem 26E
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- Skip ! A bag contains 5 red balls, 3 blue balls, and 2 green balls. Two balls are drawn one after the other without replacement. What is the probability that both balls are red?Hint: Multiply probabilities for dependent events.arrow_forwardIn a population of 1000 people, the ages are normally distributed with a mean of 30 years and a standard deviation of 10 years. What is the probability that a randomly selected person is older than 40?Hint: Calculate the Z-score and look up the value in the standard normal table.arrow_forwardIn a standard deck of 52 playing cards, what is the probability of drawing a queen or a heart?Hint: Use the addition rule of probability and account for overlapping events.arrow_forward
- do not answer without proper knowledge! A box contains 3 red, 4 blue, and 5 green balls. One ball is drawn at random. What is the probability that the ball drawn is either blue or green?Hint: Total probability for two outcomes.arrow_forwardDo not use ChatGPT! The mean of a dataset is 20 and the standard deviation is 4. What percentage of the data lies between 12 and 28, assuming a normal distribution?Hint: Use the Empirical Rule or Z-scores for more precision.arrow_forwardSkip All ! A fair die is rolled 3 times. What is the probability of getting at least one "6" in the three rolls?Hint: Use the complement rule.arrow_forward
- No AI ! A dataset follows a normal distribution with a mean of 50 and a standard deviation of 5. What is the probability that a randomly selected value is between 45 and 55?arrow_forwardob. 1 (2 points). Let x(t), y(t) = C¹ (R, R) satisfy: x' = sin x, and y' = sin y and they satisfy the initial condition: = x(0) = xo, y(0) = yo. Prove that for all tЄ R: |x(t) − y(t)| ≤ |xo — Yo|et| . - - - 1 1 1arrow_forwardThis problem demonstrates a possible (though rare) situation that can occur with group comparisons. The groups are sections and the numerical variable being compared is an exam score. Section 1 Section 2 Section 3 72.9 56.6 62.1 56.6 72.1 52.1 58.6 53.8 67 63.5 46.5 62.9 50.5 29.8 60.3 67.2 68.5 63.5 69.2 32.4 59 55.5 51.4 69.5 64.4 45.6 53.8 Click Download CSV to download csv file of data or copy/paste the data into Excel. After downloading the file, you may want to save it as an Excel Workbook. a. Perform a one-way ANOVA with a = = 0.05. Report the F test statistic rounded to 3 decimal places and the P-value rounded to 4 decimal places. F= p = b. What is the conclusion from the ANOVA? O reject the null hypothesis: at least one of the group means is different O fail to reject the null hypothesis: not enough evidence to suggest the group means are different c. Calculate the group means for each section (Rounded to 2 decimal places): Section 1: 1 = Section 2:2= Section 3: 3= d. Conduct…arrow_forward
- In a batch of 2000 bulbs, 5% are defective. If 10 bulbs are selected at random, what is the probability that at least 1 is defective?arrow_forwardA class of 50 students has scores with a mean of 70 and a standard deviation of 8. Assuming normal distribution, how many students are expected to score above 78?arrow_forwardDo not answer without proper knowledge! A researcher wants to test whether the mean height of a plant species is 25 cm. A sample of 16 plants has a mean of 23.5 cm and a standard deviation of 3 cm. Perform a hypothesis test at the 5% significance level.arrow_forward
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