Some properties of Expected value and variance of a random variable. a) Assume that X is an arbitrary discrete random variable, and a and b are constant. Using the definitic Show: and E(aX + b) = a · E(X) + b V(aX + b) = a² · V(X ) Stat 3128 Ali Mahzarnia STAT 3128 Ali Mahzarnia b) Justify the computational formula of Variance of a random variable which is to justify : V(X) = E[(X – µ°] = Er– µ}° • ptx) = | Ex² - px) – µ² = E(X*) – [EX)F Σ Here needs justification
Some properties of Expected value and variance of a random variable. a) Assume that X is an arbitrary discrete random variable, and a and b are constant. Using the definitic Show: and E(aX + b) = a · E(X) + b V(aX + b) = a² · V(X ) Stat 3128 Ali Mahzarnia STAT 3128 Ali Mahzarnia b) Justify the computational formula of Variance of a random variable which is to justify : V(X) = E[(X – µ°] = Er– µ}° • ptx) = | Ex² - px) – µ² = E(X*) – [EX)F Σ Here needs justification
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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![2. Some properties of Expected value and variance of a random variable.
a) Assume that X is an arbitrary discrete random variable, and a and b are constant. Using the definitic
Show:
and
E(aX + b) = a · E(X) + b
V(aX + b) = a² · V(X )
Stat 3128 Ali Mahzarnia
P
STAT 3128
Ali Mahzarnia
b) Justify the computational formula of Variance of a random variable which is to justify :
V(X) = E[(X – µ°] = Ex – µ)P • ptx) = | 2:
Here needs
justification
By Cauchy Schwarz inequality it can be shown that the right hand side is always positive.
Analogs expression in Mechanic : Parallel axis theorem
Iem
= I– md²
Moment of
Moment of
inetria about
Inertia of an
an axis shifted
object about the
center of a mass
by d from
center of mass
(a parallel shift)
Icm is dispersion around the mean and is like second central moment
(variance) I is like second moment if d is mean
m is like sum total all the weight of each of the x which all add up to 1
d squared is like squared of mean since we,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F072e444d-1bde-4899-b3c3-9f07885f3d58%2Fd9be63b1-98d9-4bd5-89f1-753c0c16d5d7%2Fmesf1wf_processed.png&w=3840&q=75)
Transcribed Image Text:2. Some properties of Expected value and variance of a random variable.
a) Assume that X is an arbitrary discrete random variable, and a and b are constant. Using the definitic
Show:
and
E(aX + b) = a · E(X) + b
V(aX + b) = a² · V(X )
Stat 3128 Ali Mahzarnia
P
STAT 3128
Ali Mahzarnia
b) Justify the computational formula of Variance of a random variable which is to justify :
V(X) = E[(X – µ°] = Ex – µ)P • ptx) = | 2:
Here needs
justification
By Cauchy Schwarz inequality it can be shown that the right hand side is always positive.
Analogs expression in Mechanic : Parallel axis theorem
Iem
= I– md²
Moment of
Moment of
inetria about
Inertia of an
an axis shifted
object about the
center of a mass
by d from
center of mass
(a parallel shift)
Icm is dispersion around the mean and is like second central moment
(variance) I is like second moment if d is mean
m is like sum total all the weight of each of the x which all add up to 1
d squared is like squared of mean since we,
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