Solution Found!
Let Y have density function a Find the value of c that
Chapter 4, Problem 165SE(choose chapter or problem)
Let 𝑌 have density function
\(f(y)=\left\{\begin{array}{ll}
c y e^{-2 y}, & 0 \leq y \leq \infty, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
a Find the value of c that makes \(f(y)\) a density function.
b Give the mean and variance for 𝑌.
c Give the moment-generating function for 𝑌.
Equation Transcription:
Text Transcription:
f(y)=
cye^-2y, 0</=y</=infinity,
0, elsewhere.
f(y)
Questions & Answers
QUESTION:
Let 𝑌 have density function
\(f(y)=\left\{\begin{array}{ll}
c y e^{-2 y}, & 0 \leq y \leq \infty, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
a Find the value of c that makes \(f(y)\) a density function.
b Give the mean and variance for 𝑌.
c Give the moment-generating function for 𝑌.
Equation Transcription:
Text Transcription:
f(y)=
cye^-2y, 0</=y</=infinity,
0, elsewhere.
f(y)
ANSWER:
Solution 165SE
Step1 of 4:
Let us consider a random variable Y with density function:
Here our goal is:
a). We need to find the value of c that makes f (y) a density function.
b). We need to give the mean and variance for Y .
c). We need to give the moment-generating function for Y .
Step2 of 4:
a).
Let,