MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Chapter 11, Problem 14P
The equation of a circle with its center is at x=3 and y=2 is given by
(x-3)2-(y-2)2=R2where R is the radius of the circle. Write a program in a script file that first derives the equation (symbolically) of the tangent line to the circle at the point (x0, y0on the upper part of the circle [i.e., for (3-R)
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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
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The analyst fits the model and obtains:
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Ŷ50,000+150X
YBoB₁X + €
•
R² = 0.76
• Residuals show a fan-shaped pattern when plotted against fitted values.
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Chapter 11 Solutions
MATLAB: An Introduction with Applications
Ch. 11 - Prob. 1PCh. 11 - Define y as a symbolic variable and create the two...Ch. 11 - Define x and y as symbolic variables and create...Ch. 11 - Define x as a symbolic variable. (a) Derive the...Ch. 11 - Use the commands from Section 11.2 to show that:...Ch. 11 - Use the commands from Section 11.2 to show that:...Ch. 11 - In rectangular coordinates the equation of the...Ch. 11 - Prob. 8PCh. 11 - The relation between the tension T and the steady...Ch. 11 - Consider the two ellipses in the x y plane given...
Ch. 11 - A 120 in.-long beam AB is attached to the wall...Ch. 11 - A box of mass m is being pulled by a rope as...Ch. 11 - The mechanical power output P in a contracting...Ch. 11 - The equation of a circle with its center is at x=3...Ch. 11 - A tracking radar antenna is locked on an airplane...Ch. 11 - Prob. 16PCh. 11 - Evaluate the following indefinite integrals: (a)...Ch. 11 - Define x as a symbolic variable and create the...Ch. 11 - The one-dimensional diffusion equation is given...Ch. 11 - A ceramic tile has the design shown in the figure....Ch. 11 - Prob. 21PCh. 11 - 22. Consider the parabolic sector shown in the...Ch. 11 - Prob. 23PCh. 11 - The spread of an infection from a single...Ch. 11 - The Maxwell-Boltzmann probability density function...Ch. 11 - The velocity of a skydiver whose parachute is...Ch. 11 - 27. A resistor R (R = 0.4?) and an inductor L (L =...Ch. 11 - Determine the general solution of the differential...Ch. 11 - Determine the solution of the following...Ch. 11 - 30. The current, i, in a series RLC circuit when...Ch. 11 - Damped free vibrations can be modeled by a block...
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