Solution Found!
Let Y be a discrete random variable with mean ? and
Chapter 3, Problem 33E(choose chapter or problem)
Let be a discrete random variable with mean \(\mu\) and variance \(\sigma^{2}\). If
and
are constants, use Theorems
through
to prove that
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:
sigma2
E(aY+b)=aE(Y)+b=a mu+b
V(aY+b)=a2V(Y)=a^2 sigma^2
Questions & Answers
QUESTION:
Let be a discrete random variable with mean \(\mu\) and variance \(\sigma^{2}\). If
and
are constants, use Theorems
through
to prove that
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:
sigma2
E(aY+b)=aE(Y)+b=a mu+b
V(aY+b)=a2V(Y)=a^2 sigma^2
ANSWER:
Solution:
Step 1 of 3:
Here we need to prove that
a).
b).