Solution Found!
Solved: If Y is a continuous random variable with density
Chapter 4, Problem 37E(choose chapter or problem)
If is a continuous random variable with density function \(f(y)\) that is symmetric about 0 (that is, \(f(y)=f(-y)\) for all
) and
exists, show that \(E(Y)=0\). [Hint: \(E(Y)=\int_{-\infty}^{0} y f(y)+\int_{0}^{\infty} y f(y) d y\) Make the change of variable \(w=-y\) in the first integral.]
Equation Transcription:
Text Transcription:
f(y)
f(y)=f(-y)
E(Y)
E(Y)=0
E(Y)=integral_-infinity^0 yf(y)+integral_0^infinity yf(y)dy
w=-y
Questions & Answers
QUESTION:
If is a continuous random variable with density function \(f(y)\) that is symmetric about 0 (that is, \(f(y)=f(-y)\) for all
) and
exists, show that \(E(Y)=0\). [Hint: \(E(Y)=\int_{-\infty}^{0} y f(y)+\int_{0}^{\infty} y f(y) d y\) Make the change of variable \(w=-y\) in the first integral.]
Equation Transcription:
Text Transcription:
f(y)
f(y)=f(-y)
E(Y)
E(Y)=0
E(Y)=integral_-infinity^0 yf(y)+integral_0^infinity yf(y)dy
w=-y
ANSWER:
Solution :
Step 1 of 1:
Let Y is a continuous random variable with density function f(y) that is symmetric about 0
Our goal is:
We need to show that E(Y)=.