Homework Help is Here – Start Your Trial Now!
Math
Statistics
Say we have a continuous random variable X. Let ƒ(x) = c(1 + x²) for support S = [0,1] and c being a constant. What value of c will make this a valid density function? Round to the nearest 2nd decimal place, x.xx

Say we have a continuous random variable X. Let ƒ(x) = c(1 + x²) for support S = [0,1] and c being a constant. What value of c will make this a valid density function? Round to the nearest 2nd decimal place, x.xx

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
See similar textbooks
icon
Related questions
Question
### Continuous Random Variable Density Function We consider a continuous random variable \( X \). Define the probability density function \( f(x) = c(1 + x^2) \) over the support \( S_x = [0, 1] \), with \( c \) being a constant. The problem is to determine the value of \( c \) that will make \( f(x) \) a valid density function. To find \( c \), the integral of \( f(x) \) over the support \( S_x \) must equal 1: \[ \int_{0}^{1} f(x) \, dx = 1. \] Given \( f(x) = c(1 + x^2) \): \[ \int_{0}^{1} c(1 + x^2) \, dx = 1. \] Solving this integral will give us the required value of \( c \). Round the value of \( c \) to the nearest 2nd decimal place, \( x.xx \).
Transcribed Image Text:### Continuous Random Variable Density Function We consider a continuous random variable \( X \). Define the probability density function \( f(x) = c(1 + x^2) \) over the support \( S_x = [0, 1] \), with \( c \) being a constant. The problem is to determine the value of \( c \) that will make \( f(x) \) a valid density function. To find \( c \), the integral of \( f(x) \) over the support \( S_x \) must equal 1: \[ \int_{0}^{1} f(x) \, dx = 1. \] Given \( f(x) = c(1 + x^2) \): \[ \int_{0}^{1} c(1 + x^2) \, dx = 1. \] Solving this integral will give us the required value of \( c \). Round the value of \( c \) to the nearest 2nd decimal place, \( x.xx \).
Expert Solution
steps

Step by step

Solved in 3 steps with 16 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS