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
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]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F72fc51e3-4382-4f11-b367-046c9ce529b0%2F6f461ef6-029e-4911-b978-e8557f7c4f7b%2Fvd2m4yq_processed.jpeg&w=3840&q=75)
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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