EBK MATLAB: AN INTRODUCTION WITH APPLIC
6th Edition
ISBN: 8220103113663
Author: GILAT
Publisher: YUZU
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Chapter 8, Problem 2P
Plot the polynomial
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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 8 Solutions
EBK MATLAB: AN INTRODUCTION WITH APPLIC
Ch. 8 - Prob. 1PCh. 8 - Plot the polynomial y=0.7x413.5x2+6x37 in the...Ch. 8 - Determine the polynomial y(x) that has roots at x...Ch. 8 - Use MATLAB to carry out the following...Ch. 8 - Use MATLAB to carry out the following...Ch. 8 - Use MATLAB to divide the polynomial...Ch. 8 - Use MATLAB to divide the ploynomial...Ch. 8 - The product of four consecutive even integers is...Ch. 8 - The product of three integers with spacing of 3...Ch. 8 - The product of three distinct integers is 6240....
Ch. 8 - A rectangular steel container (no top) has the...Ch. 8 - An aluminum container has the geometry shown in...Ch. 8 - A rectangular box (no top) is welded together...Ch. 8 - The probability P of selecting three distinct...Ch. 8 - Write a user-defined function that adds or...Ch. 8 - Write a user-defined function that multiplies two...Ch. 8 - Write a user-defined function that calculates the...Ch. 8 - A cylinder with base radius rand height h is...Ch. 8 - Consider the parabola: x = 2(y-2)2 +3,and the...Ch. 8 - The following data is given: x -5 -4 -1 1 4 6 9 10...Ch. 8 - 21. The boiling temperature of water TB at various...Ch. 8 - The U.S. population in selected years between 1815...Ch. 8 - The number of bacteria NBmeasured at different...Ch. 8 - Growth data of a sunflower plant is given tn the...Ch. 8 - Use the growth data from Problem 24 for the...Ch. 8 - 26. The following points are given: x 1 2.2 3.7...Ch. 8 - The standard air density. D (average of...Ch. 8 - Write a user-defined function that determines the...Ch. 8 - Estimated values of thermal conductivity of...Ch. 8 - Measurements of the concentration, C, of a...Ch. 8 - Use the data from Problem 30 for the following:...Ch. 8 - The relationship between two variables y and x is...Ch. 8 - Curve-lit the data from the previous problem with...Ch. 8 - When rubber is stretched, its elongation is...Ch. 8 - The transmission of light through a transparent...
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