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Question 4: (a) In statistics, the normal or Gaussian density function is defined by f(x) = 1 -(x-1)2 e 202 σπ in the interval (-co, co). Prove that (i) f (x)dx = 1 (ii) xf (x)dx = p (iii) (i) x2f(x)dx = σ² +μ² [3] (b) Define definite and and indefinite integral. Also write the properties of indefinite integral. [2]

Question 4: (a) In statistics, the normal or Gaussian density function is defined by f(x) = 1 -(x-1)2 e 202 σπ in the interval (-co, co). Prove that (i) f (x)dx = 1 (ii) xf (x)dx = p (iii) (i) x2f(x)dx = σ² +μ² [3] (b) Define definite and and indefinite integral. Also write the properties of indefinite integral. [2]

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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Question 4: (a) In statistics, the normal or Gaussian density function is defined by f(x) = 1 -(x-1)2 e 202 σπ in the interval (-co, co). Prove that (i) f (x)dx = 1 (ii) xf (x)dx = p (iii) (i) x2f(x)dx = σ² +μ² [3] (b) Define definite and and indefinite integral. Also write the properties of indefinite integral. [2]
Transcribed Image Text:Question 4: (a) In statistics, the normal or Gaussian density function is defined by f(x) = 1 -(x-1)2 e 202 σπ in the interval (-co, co). Prove that (i) f (x)dx = 1 (ii) xf (x)dx = p (iii) (i) x2f(x)dx = σ² +μ² [3] (b) Define definite and and indefinite integral. Also write the properties of indefinite integral. [2]
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