Basic Technical Mathematics
11th Edition
ISBN: 9780134437705
Author: Washington
Publisher: PEARSON
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Chapter 30.3, Problem 4E
To determine
The Maclaurin expansion of
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answer number 4
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.
answer number 6
Chapter 30 Solutions
Basic Technical Mathematics
Ch. 30.1 - Prob. 1PECh. 30.1 - Prob. 2PECh. 30.1 - Prob. 1ECh. 30.1 - Prob. 2ECh. 30.1 - Prob. 3ECh. 30.1 - Prob. 4ECh. 30.1 - Prob. 5ECh. 30.1 - Prob. 6ECh. 30.1 - Prob. 7ECh. 30.1 - Prob. 8E
Ch. 30.1 - Prob. 9ECh. 30.1 - Prob. 10ECh. 30.1 - Prob. 11ECh. 30.1 - Prob. 12ECh. 30.1 - Prob. 13ECh. 30.1 - Prob. 14ECh. 30.1 - Prob. 15ECh. 30.1 - Prob. 16ECh. 30.1 - Prob. 17ECh. 30.1 - Prob. 18ECh. 30.1 - Prob. 19ECh. 30.1 - Prob. 20ECh. 30.1 - Prob. 21ECh. 30.1 - Prob. 22ECh. 30.1 - Prob. 23ECh. 30.1 - Prob. 24ECh. 30.1 - Prob. 25ECh. 30.1 - Prob. 26ECh. 30.1 - Prob. 27ECh. 30.1 - Prob. 28ECh. 30.1 - Prob. 29ECh. 30.1 - Prob. 30ECh. 30.1 - Prob. 31ECh. 30.1 - Prob. 32ECh. 30.1 - Prob. 33ECh. 30.1 - Prob. 34ECh. 30.1 - Prob. 35ECh. 30.1 - Prob. 36ECh. 30.1 - Prob. 37ECh. 30.1 - Prob. 38ECh. 30.1 - Prob. 39ECh. 30.1 - Prob. 40ECh. 30.1 - Prob. 41ECh. 30.1 - In Exercises 39–48, solve the given problems as...Ch. 30.1 - Prob. 43ECh. 30.1 - Prob. 44ECh. 30.1 - In Exercises 39–48, solve the given problems as...Ch. 30.1 - Prob. 46ECh. 30.1 - Prob. 47ECh. 30.1 - Prob. 48ECh. 30.2 - Find the first four terms of the Maclaurin series...Ch. 30.2 - Prob. 1ECh. 30.2 - Prob. 2ECh. 30.2 - Prob. 3ECh. 30.2 - Prob. 4ECh. 30.2 - Prob. 5ECh. 30.2 - Prob. 6ECh. 30.2 - Prob. 7ECh. 30.2 - Prob. 8ECh. 30.2 - Prob. 9ECh. 30.2 - Prob. 10ECh. 30.2 - Prob. 11ECh. 30.2 - Prob. 12ECh. 30.2 - Prob. 13ECh. 30.2 - Prob. 14ECh. 30.2 - Prob. 15ECh. 30.2 - Prob. 16ECh. 30.2 - Prob. 17ECh. 30.2 - Prob. 18ECh. 30.2 - Prob. 19ECh. 30.2 - Prob. 20ECh. 30.2 - Prob. 21ECh. 30.2 - Prob. 22ECh. 30.2 - Prob. 23ECh. 30.2 - Prob. 24ECh. 30.2 - Prob. 25ECh. 30.2 - Prob. 26ECh. 30.2 - Prob. 27ECh. 30.2 - In Exercises 21–28, find the first two nonzero...Ch. 30.2 - Prob. 29ECh. 30.2 - Prob. 30ECh. 30.2 - In Exercises 29–44, solve the given problems.
Is...Ch. 30.2 - In Exercises 29–44, solve the given problems.
Is...Ch. 30.2 - Prob. 33ECh. 30.2 - Prob. 34ECh. 30.2 - Prob. 35ECh. 30.2 - Prob. 36ECh. 30.2 - In Exercises 29–44, solve the given problems.
The...Ch. 30.2 - Prob. 38ECh. 30.2 - Prob. 39ECh. 30.2 - Prob. 40ECh. 30.2 - Prob. 41ECh. 30.2 - Prob. 42ECh. 30.2 - Prob. 43ECh. 30.2 - Prob. 44ECh. 30.3 - Using the Maclaurin series for ln(1 + x), find the...Ch. 30.3 - Prob. 2PECh. 30.3 - Prob. 1ECh. 30.3 - Prob. 2ECh. 30.3 - Prob. 3ECh. 30.3 - Prob. 4ECh. 30.3 - Prob. 5ECh. 30.3 - In Exercises 3–10, find the first four nonzero...Ch. 30.3 - Prob. 7ECh. 30.3 - Prob. 8ECh. 30.3 - In Exercises 3–10, find the first four nonzero...Ch. 30.3 - Prob. 10ECh. 30.3 - Prob. 11ECh. 30.3 - Prob. 12ECh. 30.3 - In Exercises 11–16, evaluate the given integrals...Ch. 30.3 - Prob. 14ECh. 30.3 - Prob. 15ECh. 30.3 - Prob. 16ECh. 30.3 - Prob. 17ECh. 30.3 - Prob. 18ECh. 30.3 - In Exercises 17–30, find the indicated series by...Ch. 30.3 - Prob. 20ECh. 30.3 - Prob. 21ECh. 30.3 - In Exercises 17–30, find the indicated series by...Ch. 30.3 - Prob. 23ECh. 30.3 - Prob. 24ECh. 30.3 - Prob. 25ECh. 30.3 - Prob. 26ECh. 30.3 - Prob. 27ECh. 30.3 - Prob. 28ECh. 30.3 - Prob. 29ECh. 30.3 - Prob. 30ECh. 30.3 - Prob. 31ECh. 30.3 - Prob. 32ECh. 30.3 - Prob. 33ECh. 30.3 - Prob. 34ECh. 30.3 - Prob. 35ECh. 30.3 - Prob. 36ECh. 30.3 - Prob. 37ECh. 30.3 - Prob. 38ECh. 30.3 - Prob. 39ECh. 30.3 - Prob. 40ECh. 30.3 - Prob. 41ECh. 30.3 - Prob. 42ECh. 30.3 - Prob. 43ECh. 30.3 - Prob. 44ECh. 30.3 - Prob. 45ECh. 30.3 - Prob. 46ECh. 30.4 - Using three terms of the appropriate series,...Ch. 30.4 - Prob. 2PECh. 30.4 - Prob. 1ECh. 30.4 - Prob. 2ECh. 30.4 - Prob. 3ECh. 30.4 - Prob. 4ECh. 30.4 - Prob. 5ECh. 30.4 - Prob. 6ECh. 30.4 - Prob. 7ECh. 30.4 - Prob. 8ECh. 30.4 - Prob. 9ECh. 30.4 - Prob. 10ECh. 30.4 - Prob. 11ECh. 30.4 - Prob. 12ECh. 30.4 - In Exercises 3–20, calculate the value of each of...Ch. 30.4 - Prob. 14ECh. 30.4 - Prob. 15ECh. 30.4 - Prob. 16ECh. 30.4 - Prob. 17ECh. 30.4 - Prob. 18ECh. 30.4 - Prob. 19ECh. 30.4 - Prob. 20ECh. 30.4 - Prob. 21ECh. 30.4 - Prob. 22ECh. 30.4 - Prob. 23ECh. 30.4 - Prob. 24ECh. 30.4 - Prob. 25ECh. 30.4 - Prob. 26ECh. 30.4 - Prob. 27ECh. 30.4 - Prob. 28ECh. 30.4 - Prob. 29ECh. 30.4 - Prob. 30ECh. 30.4 - Prob. 31ECh. 30.4 - Prob. 32ECh. 30.4 - Prob. 33ECh. 30.4 - Prob. 34ECh. 30.4 - Prob. 35ECh. 30.4 - Prob. 36ECh. 30.4 - In Exercises 29–40, solve the given problems by...Ch. 30.4 - Prob. 38ECh. 30.4 - Prob. 39ECh. 30.4 - Prob. 40ECh. 30.5 - Expand f(x) = ex in a Taylor series with a = 3.
Ch. 30.5 - Prob. 1ECh. 30.5 - Prob. 2ECh. 30.5 - Prob. 3ECh. 30.5 - Prob. 4ECh. 30.5 - Prob. 5ECh. 30.5 - Prob. 6ECh. 30.5 - Prob. 7ECh. 30.5 - Prob. 8ECh. 30.5 - Prob. 9ECh. 30.5 - Prob. 10ECh. 30.5 - In Exercises 11–22, find the first three nonzero...Ch. 30.5 - Prob. 12ECh. 30.5 - Prob. 13ECh. 30.5 - Prob. 14ECh. 30.5 - Prob. 15ECh. 30.5 - Prob. 16ECh. 30.5 - In Exercises 11–22, find the first three nonzero...Ch. 30.5 - In Exercises 11–22, find the first three nonzero...Ch. 30.5 - Prob. 19ECh. 30.5 - Prob. 20ECh. 30.5 - Prob. 21ECh. 30.5 - Prob. 22ECh. 30.5 - Prob. 23ECh. 30.5 - Prob. 24ECh. 30.5 - Prob. 25ECh. 30.5 - Prob. 26ECh. 30.5 - Prob. 27ECh. 30.5 - Prob. 28ECh. 30.5 - Prob. 29ECh. 30.5 - Prob. 30ECh. 30.5 - Prob. 31ECh. 30.5 - Prob. 33ECh. 30.5 - Prob. 34ECh. 30.5 - In Exercises 31–38, solve the given...Ch. 30.5 - Prob. 36ECh. 30.5 - In Exercises 31–38, solve the given...Ch. 30.5 - Prob. 38ECh. 30.5 - In Exercises 39–42, use a calculator to display...Ch. 30.5 - In Exercises 39–42, use a calculator to display...Ch. 30.5 - In Exercises 39–42, use a calculator to display...Ch. 30.5 - In Exercises 39–42, use a calculator to display...Ch. 30.6 - In Example 2, in the definition of f(x), replace 1...Ch. 30.6 - Prob. 1ECh. 30.6 - Prob. 2ECh. 30.6 - In Exercises 3–14, find at least three nonzero...Ch. 30.6 - Prob. 4ECh. 30.6 - In Exercises 3–14, find at least three nonzero...Ch. 30.6 - Prob. 6ECh. 30.6 - In Exercises 3–14, find at least three nonzero...Ch. 30.6 - Prob. 8ECh. 30.6 - In Exercises 3–14, find at least three nonzero...Ch. 30.6 - Prob. 10ECh. 30.6 - Prob. 11ECh. 30.6 - Prob. 12ECh. 30.6 - Prob. 13ECh. 30.6 - Prob. 14ECh. 30.6 - Prob. 15ECh. 30.6 - Prob. 16ECh. 30.6 - Prob. 17ECh. 30.6 - Prob. 18ECh. 30.6 - Prob. 19ECh. 30.6 - Prob. 20ECh. 30.6 - In Exercises 21–24, solve the given problems.
21....Ch. 30.6 - In Exercises 21–24, solve the given problems.
22....Ch. 30.6 - In Exercises 21–24, solve the given problems.
23....Ch. 30.6 - Prob. 24ECh. 30.7 - Determine whether the following functions are even...Ch. 30.7 - Prob. 2PECh. 30.7 - Prob. 3PECh. 30.7 - In Exercises 1–4, write the Fourier series for...Ch. 30.7 - In Exercises 1–4, write the Fourier series for...Ch. 30.7 - In Exercises 1–4, write the Fourier series for...Ch. 30.7 - In Exercises 1–4, write the Fourier series for...Ch. 30.7 - In Exercises 5−12, determine whether the given...Ch. 30.7 - In Exercises 5–12, determine whether the given...Ch. 30.7 - In Exercises 5–12, determine whether the given...Ch. 30.7 - In Exercises 5–12, determine whether the given...Ch. 30.7 - In Exercises 5–12, determine whether the given...Ch. 30.7 - In Exercises 5–12, determine whether the given...Ch. 30.7 - In Exercises 5–12, determine whether the given...Ch. 30.7 - In Exercises 5–12, determine whether the given...Ch. 30.7 - In Exercises 13–16, determine whether the Fourier...Ch. 30.7 - In Exercises 13–16, determine whether the Fourier...Ch. 30.7 - In Exercises 13–16, determine whether the Fourier...Ch. 30.7 - In Exercises 13–16, determine whether the Fourier...Ch. 30.7 - Prob. 17ECh. 30.7 - Prob. 18ECh. 30.7 - Prob. 19ECh. 30.7 - Prob. 20ECh. 30.7 - Prob. 21ECh. 30.7 - Prob. 22ECh. 30.7 - Prob. 23ECh. 30.7 - Prob. 24ECh. 30.7 - Prob. 25ECh. 30.7 - Prob. 26ECh. 30.7 - Prob. 27ECh. 30.7 - In Exercises 23–28, solve the given problems.
28....Ch. 30 - Prob. 1RECh. 30 - Prob. 2RECh. 30 - Prob. 3RECh. 30 - Prob. 4RECh. 30 - Prob. 5RECh. 30 - Prob. 6RECh. 30 - Prob. 7RECh. 30 - Prob. 8RECh. 30 - Prob. 9RECh. 30 - Prob. 10RECh. 30 - Prob. 11RECh. 30 - Prob. 12RECh. 30 - Prob. 13RECh. 30 - Prob. 14RECh. 30 - Prob. 15RECh. 30 - Prob. 16RECh. 30 - Prob. 17RECh. 30 - Prob. 18RECh. 30 - Prob. 19RECh. 30 - Prob. 20RECh. 30 - Prob. 21RECh. 30 - Prob. 22RECh. 30 - Prob. 23RECh. 30 - Prob. 24RECh. 30 - Prob. 25RECh. 30 - Prob. 26RECh. 30 - Prob. 27RECh. 30 - Prob. 28RECh. 30 - Prob. 29RECh. 30 - Prob. 30RECh. 30 - Prob. 31RECh. 30 - Prob. 32RECh. 30 - Prob. 33RECh. 30 - Prob. 34RECh. 30 - Prob. 35RECh. 30 - Prob. 36RECh. 30 - Prob. 37RECh. 30 - Prob. 38RECh. 30 - Prob. 39RECh. 30 - Prob. 40RECh. 30 - Prob. 41RECh. 30 - Prob. 42RECh. 30 - Prob. 43RECh. 30 - Prob. 44RECh. 30 - Prob. 45RECh. 30 - Prob. 46RECh. 30 - Prob. 47RECh. 30 - Prob. 48RECh. 30 - Prob. 49RECh. 30 - Prob. 50RECh. 30 - Prob. 51RECh. 30 - Prob. 52RECh. 30 - Prob. 53RECh. 30 - Prob. 54RECh. 30 - Prob. 55RECh. 30 - In Exercises 43–80, solve the given...Ch. 30 - Prob. 57RECh. 30 - Prob. 58RECh. 30 - Prob. 59RECh. 30 - Prob. 60RECh. 30 - Prob. 61RECh. 30 - Prob. 62RECh. 30 - Prob. 63RECh. 30 - Prob. 64RECh. 30 - Prob. 65RECh. 30 - Prob. 66RECh. 30 - Prob. 67RECh. 30 - Prob. 68RECh. 30 - Prob. 69RECh. 30 - Prob. 70RECh. 30 - Prob. 71RECh. 30 - Prob. 72RECh. 30 - Prob. 73RECh. 30 - Prob. 74RECh. 30 - Prob. 75RECh. 30 - Prob. 76RECh. 30 - Prob. 77RECh. 30 - Prob. 78RECh. 30 - Prob. 79RECh. 30 - Prob. 80RECh. 30 - Prob. 81RECh. 30 - Prob. 1PTCh. 30 - Prob. 2PTCh. 30 - Prob. 3PTCh. 30 - Prob. 4PTCh. 30 - Prob. 5PTCh. 30 - Prob. 6PTCh. 30 - Prob. 7PT
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