Solution Found!
If Y is a continuous random variable with density function
Chapter 4, Problem 24E(choose chapter or problem)
QUESTION:
If is a continuous random variable with density function \(f(y)\), use Theorem
to prove that \(\sigma^{2}=V(Y)=E\left(Y^{2}\right)-[E(Y)]^{2}\).
Equation Transcription:
Text Transcription:
f(y)
sigma^2=V(Y)=E(Y^2)-[E(Y)]^2
Questions & Answers
QUESTION:
If is a continuous random variable with density function \(f(y)\), use Theorem
to prove that \(\sigma^{2}=V(Y)=E\left(Y^{2}\right)-[E(Y)]^{2}\).
Equation Transcription:
Text Transcription:
f(y)
sigma^2=V(Y)=E(Y^2)-[E(Y)]^2
ANSWER:
Solution:
Step 1 of 2:
Let Y be a continuous random variable with density f(y).
By using the different properties, we have to prove that