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A random variable x has a probability density function f(x) = 1 o√2x (² o=2. The probability that x takes values between a = 8 and b = 14 can be calculated using this integration P = f f(x)dx. Please estimate the probability using the numerical techniques we learned (i.e., Trapezoidal rule, Simpson's 1/3 rule, and Gauss quadrature method). For Trapezoidal rule and Simpson's 1/3 rule, consider 3 intervals of equal interval size. Trapezoidal rule: The required number (N) of evaluations of f(x) for the numerical integration is N = estimate of the probability P= Simpson's 1/3 rule: The required number (N) of evaluations of f(x) for the numerical integration is N = estimate of the probability P = C For Gauss quadrature, consider 3 integration points. Gauss quadrature: The required number (N) of evaluations of f(x) for the numerical integration is N = estimate of the probability P = The Gauss points and their weights are given in the following table: i ti 1 -√2/0/3/1 2 0 3 30 no V5 Wi 5 with mean = 11 and standard deviation 9 8 9 3 5 9 the : the the

A random variable x has a probability density function f(x) = 1 o√2x (² o=2. The probability that x takes values between a = 8 and b = 14 can be calculated using this integration P = f f(x)dx. Please estimate the probability using the numerical techniques we learned (i.e., Trapezoidal rule, Simpson's 1/3 rule, and Gauss quadrature method). For Trapezoidal rule and Simpson's 1/3 rule, consider 3 intervals of equal interval size. Trapezoidal rule: The required number (N) of evaluations of f(x) for the numerical integration is N = estimate of the probability P= Simpson's 1/3 rule: The required number (N) of evaluations of f(x) for the numerical integration is N = estimate of the probability P = C For Gauss quadrature, consider 3 integration points. Gauss quadrature: The required number (N) of evaluations of f(x) for the numerical integration is N = estimate of the probability P = The Gauss points and their weights are given in the following table: i ti 1 -√2/0/3/1 2 0 3 30 no V5 Wi 5 with mean = 11 and standard deviation 9 8 9 3 5 9 the : the the

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A random variable x has a probability density function f(x)=√e²²(² 1 o=2. The probability that x takes values between a = 8 and b = 14 can be calculated using this integration P = f f(x) dx. Please estimate the probability using the numerical techniques we learned (i.e., Trapezoidal rule, Simpson's 1/3 rule, and Gauss quadrature method). For Trapezoidal rule and Simpson's 1/3 rule, consider 3 intervals of equal interval size. Trapezoidal rule: The required number (N) of evaluations of f(x) for the numerical integration is N = estimate of the probability P = Simpson's 1/3 rule: The required number (N) of evaluations of f(x) for the numerical integration is N =; the estimate of the probability P = For Gauss quadrature, consider 3 integration points. Gauss quadrature: The required number (N) of evaluations of f(x) for the numerical integration is N = estimate of the probability P = The Gauss points and their weights are given in the following table: i 2 3 0 3 3 تمام 5 Wi 5 9 alanla with mean = 11 and standard deviation 8 9 5 9 the the
Transcribed Image Text:A random variable x has a probability density function f(x)=√e²²(² 1 o=2. The probability that x takes values between a = 8 and b = 14 can be calculated using this integration P = f f(x) dx. Please estimate the probability using the numerical techniques we learned (i.e., Trapezoidal rule, Simpson's 1/3 rule, and Gauss quadrature method). For Trapezoidal rule and Simpson's 1/3 rule, consider 3 intervals of equal interval size. Trapezoidal rule: The required number (N) of evaluations of f(x) for the numerical integration is N = estimate of the probability P = Simpson's 1/3 rule: The required number (N) of evaluations of f(x) for the numerical integration is N =; the estimate of the probability P = For Gauss quadrature, consider 3 integration points. Gauss quadrature: The required number (N) of evaluations of f(x) for the numerical integration is N = estimate of the probability P = The Gauss points and their weights are given in the following table: i 2 3 0 3 3 تمام 5 Wi 5 9 alanla with mean = 11 and standard deviation 8 9 5 9 the the
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