Question 7 Consider a random variable, X whose probability density function is given by (a) (b) (c) (d) f(x) = {B (-x)(x- (B (-x)(x − 3)(x²+x+1), 0≤x≤3 otherwise Show that (-x)(x-3)(x²+x+1)= − x² + 2x² + 2x² + 3x Calculate the value of By considering the sign of each factor of f(x). show that f(x) is a well-defined probability function. Hint: Do NOT multiply out f(x). Show that the Expected Value (mean) of X, E(X) is
Question 7 Consider a random variable, X whose probability density function is given by (a) (b) (c) (d) f(x) = {B (-x)(x- (B (-x)(x − 3)(x²+x+1), 0≤x≤3 otherwise Show that (-x)(x-3)(x²+x+1)= − x² + 2x² + 2x² + 3x Calculate the value of By considering the sign of each factor of f(x). show that f(x) is a well-defined probability function. Hint: Do NOT multiply out f(x). Show that the Expected Value (mean) of X, E(X) is
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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Transcribed Image Text:Question 7
Consider a random variable, X whose probability density function is given by
f(x) = {B (−x)(x − 3)(x² + x + 1).
0,
Show that (-x)(x-3)(x² + x + 1) = − x² + 2x² + 2x² + 3x
(8)
(b)
(c)
(d)
Calculate the value of
0≤x≤3
otherwise
By considering the sign of each factor of f(x). show that f(x) is a well-defined probability
function. Hint: Do NOT multiply out f(x).
Show that the Expected Value (mean) of X, E(X) is
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