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Suppose you work for a statistics company and have been tasked to develop an efficient way of evaluating the Cumulative Distribution Function (CDF) of a normal random variable. In order to do this, you come up with a method based on Huen's method and regression. . Therefore the CDF is given by The probability density function of a normally distributed variable, X ~ N (0, 1) , is given by p (x):=- 27 -S dx. Let y (t):=P(X

Suppose you work for a statistics company and have been tasked to develop an efficient way of evaluating the Cumulative Distribution Function (CDF) of a normal random variable. In order to do this, you come up with a method based on Huen's method and regression. . Therefore the CDF is given by The probability density function of a normally distributed variable, X ~ N (0, 1) , is given by p (x):=- 27 -S dx. Let y (t):=P(X

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Suppose you work for a statistics company and have been tasked to develop an efficient way of evaluating the Cumulative Distribution Function (CDF) of a normal random variable. In order to do this, you come up with a method based on Huen's method and regression. x2 1 The probability density function of a normally distributed variable, X ~ N (0,1). is given by p (x):= 2. Therefore the CDF is given by -e x2 1 P(X <1) = 2 dx. Let y (t):=P(X <t)· Argue that y solves the following IVP: - 00 12 y'(t) = 27 , у (0) —0.5. V Use Huen's method with step size h =0.1 to fill in the following table: 0.1 0.2 0.3 0.4 0.5 y(t) Use the least squared method to fit the following polynomial function to the data in the above table: p(t) =a,+a,t + a,r²+a,t³. What does your regression model predict the value of p (X <t) is at 1=0.227? Write your answer to four decimal places.
Transcribed Image Text:Suppose you work for a statistics company and have been tasked to develop an efficient way of evaluating the Cumulative Distribution Function (CDF) of a normal random variable. In order to do this, you come up with a method based on Huen's method and regression. x2 1 The probability density function of a normally distributed variable, X ~ N (0,1). is given by p (x):= 2. Therefore the CDF is given by -e x2 1 P(X <1) = 2 dx. Let y (t):=P(X <t)· Argue that y solves the following IVP: - 00 12 y'(t) = 27 , у (0) —0.5. V Use Huen's method with step size h =0.1 to fill in the following table: 0.1 0.2 0.3 0.4 0.5 y(t) Use the least squared method to fit the following polynomial function to the data in the above table: p(t) =a,+a,t + a,r²+a,t³. What does your regression model predict the value of p (X <t) is at 1=0.227? Write your answer to four decimal places.
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