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A random variable Y has the density function a Find E(e3Y
Chapter 4, Problem 145E(choose chapter or problem)
A random variable 𝑌 has the density function
\(f(y)=\left\{\begin{array}{ll}
e^{y}, & y<0, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
a Find \(E\left(e^{3 Y / 2}\right)\).
b Find the moment-generating function for 𝑌.
c Find \(V(Y)\).
Equation Transcription:
Text Transcription:
Questions & Answers
QUESTION:
A random variable 𝑌 has the density function
\(f(y)=\left\{\begin{array}{ll}
e^{y}, & y<0, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
a Find \(E\left(e^{3 Y / 2}\right)\).
b Find the moment-generating function for 𝑌.
c Find \(V(Y)\).
Equation Transcription:
Text Transcription:
ANSWER:
Answer:
Step 1 of 3:
(a)
Suppose that has a probability density function,
We need to find
The expected value of a is
………….(1)
Provided that the integral exists.
Hence using equation (1), we can write,
[since function exists from to
]
Hence the expectation is