Gaussians An important function in statistics is the

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Problem 75E Chapter 7.7

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 75E

Gaussians An important function in statistics is the Gaussian (or normal distribution, or bell-shaped curve), .

a. Graph the Gaussian for a =0.5, 1, and 2.

b. Given that , compute the area under the curves in part (a).

c. Complete the square to evaluate , where a > 0, b, and c are real numbers.

Step-by-Step Solution:
Step 1 of 3

Problem 75E

Gaussians An important function in statistics is the Gaussian (or normal distribution, or bell-shaped curve), .

a. Graph the Gaussian for a =0.5, 1, and 2.

b. Given that , compute the area under the curves in part (a).

c. Complete the square to evaluate , where a > 0, b, and c are real numbers.

Answer;

     Step-1;

 Given gaussian function is; f(x) = .

     

            Now , we have to sketch the  graph the Gaussian for a = 0.5, 1, and 2. 

       

          If a = 0.5 , then  the  graph of  the Gaussian function y=  is;

                                     

   If a = 1 , then  the  graph of  the Gaussian function y=  is ;

                                           

 

 If a = 2 , then  the  graph of  the Gaussian function y=  is ;

                                                     

Step-2;

         b)     Given that  dx =  

           Now , we have to find out the area under the curves in part (a).

                       We know that  dx =   means area under the curve between , and x -axis is .

      Therefore, the area under the curve between , and x -axis is;

                                             dx = .Since a = 0.5

         Thus ,  the area under the curve between , and x -axis is;

                                             dx = .Since a = 1

       Therefore ,  the area under the curve between , and x -axis is;

                                             dx =

Step 2 of 3

Chapter 7.7, Problem 75E is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

The answer to “Gaussians An important function in statistics is the Gaussian (or normal distribution, or bell-shaped curve), .a. Graph the Gaussian for a =0.5, 1, and 2.________________b. Given that , compute the area under the curves in part (a).________________c. Complete the square to evaluate , where a > 0, b, and c are real numbers.” is broken down into a number of easy to follow steps, and 53 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: gaussian, given, complete, compute, curve. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Calculus: Early Transcendentals was written by Sieva Kozinsky and is associated to the ISBN: 9780321570567. The full step-by-step solution to problem: 75E from chapter: 7.7 was answered by Sieva Kozinsky, our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 75E from 7.7 chapter was answered, more than 246 students have viewed the full step-by-step answer.

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