MATLAB: An Introduction with Applications
5th Edition
ISBN: 9781118629864
Author: Amos Gilat
Publisher: WILEY
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Chapter 4, Problem 12P
An isosceles triangle sign is designed to have a triangular printed area of 600 in.2 (shaded area with a base length of a and height of h in the figure). As shown in the figure, there is a 2-in. gap between the sides of the triangles. Write a MATLAB program that determine the dimensions a and h, such that the overall area of the sign will be as small as possible. In the program define a
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3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
4. Linear Regression - Model Assumptions and Interpretation
A real estate analyst is studying how house prices (Y) are related to house size in square feet (X). A simple
linear regression model is proposed:
The analyst fits the model and obtains:
•
Ŷ50,000+150X
YBoB₁X + €
•
R² = 0.76
• Residuals show a fan-shaped pattern when plotted against fitted values.
Questions:
a) Interpret the slope coefficient in context.
b) Explain what the R² value tells us about the model's performance.
c) Based on the residual pattern, what regression assumption is likely violated? What might be the
consequence?
d) Suggest at least two remedies to improve the model, based on the residual analysis.
5. Probability Distributions – Continuous Random Variables
A factory machine produces metal rods whose lengths (in cm) follow a continuous uniform distribution on the interval [98, 102].
Questions:
a) Define the probability density function (PDF) of the rod length.b) Calculate the probability that a randomly selected rod is shorter than 99 cm.c) Determine the expected value and variance of rod lengths.d) If a sample of 25 rods is selected, what is the probability that their average length is between 99.5 cm and 100.5 cm? Justify your answer using the appropriate distribution.
Chapter 4 Solutions
MATLAB: An Introduction with Applications
Ch. 4 - Prob. 1PCh. 4 - The monthly saving P that has to be deposit in a...Ch. 4 - Prob. 3PCh. 4 - The volume V and the surface area S of a...Ch. 4 - Prob. 5PCh. 4 - Prob. 6PCh. 4 -
7. A rocket flying straight up measures the...Ch. 4 - Prob. 8PCh. 4 - Prob. 9PCh. 4 - The balance of a loan, B, after n monthly payments...
Ch. 4 - Early explorers often estimated altitude by...Ch. 4 - An isosceles triangle sign is designed to have a...Ch. 4 - 13. A round billboard with radius R — 55 in. is...Ch. 4 - Prob. 14PCh. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Prob. 17PCh. 4 - The intrinsic electrical conductivity a of a...Ch. 4 - Prob. 19PCh. 4 - The net heat exchange by radiation from plate 1...Ch. 4 - Prob. 21PCh. 4 - Prob. 22PCh. 4 - Prob. 23PCh. 4 - Prob. 24PCh. 4 - The surface of many airfoils can be described with...Ch. 4 - During a golf match, a certain number of points...Ch. 4 - The dissolution of copper sulfide in aqueous...Ch. 4 - 28. The wind chill temperature, 7WC, is the air...Ch. 4 - Prob. 29P
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