Solution Found!
If Y is a continuous random variable with mean ? and
Chapter 4, Problem 26E(choose chapter or problem)
If is a continuous random variable with mean
and variance
and
and
are constants, use Theorem
to prove the following:
a \(E(a Y+b)=a E(Y)+b=a \mu+b\).
b \(V(a Y+b)=a^{2} V(Y)=a^{2} \sigma^{2}\).
Equation Transcription:
Text Transcription:
E(aY+b)=aE(Y)+b=a mu+b
V(aY+b)=a^2V(Y)=a^2 sigma^2
Questions & Answers
QUESTION:
If is a continuous random variable with mean
and variance
and
and
are constants, use Theorem
to prove the following:
a \(E(a Y+b)=a E(Y)+b=a \mu+b\).
b \(V(a Y+b)=a^{2} V(Y)=a^{2} \sigma^{2}\).
Equation Transcription:
Text Transcription:
E(aY+b)=aE(Y)+b=a mu+b
V(aY+b)=a^2V(Y)=a^2 sigma^2
ANSWER:
Solution 26E
Step1 of 3:
Let us consider a random variable Y with mean and variance
let a and b are constants.
We need to prove that:
a). E ( aY + b) = aE(Y ) + b
= aμ + b.
b). V ( aY + b) =
= .
Step2 of 3: