Solution Found!
Suppose that the waiting time for the first customer to
Chapter 4, Problem 136E(choose chapter or problem)
Suppose that the waiting time for the first customer to enter a retail shop after . is a random variable with an exponential density function given by
\(f(y)=\left\{\begin{array}{ll}
\left(\frac{1}{\theta}\right) e^{-y / \theta}, & y>0, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
a Find the moment-generating function for .
b Use the answer from part (a) to find \(E(Y)\) and \(V(Y)\).
Equation Transcription:
Text Transcription:
f(y)=
(1 over theta)e^-y/theta, y>0
0, elsewhere.
E(Y)
V(Y)
Questions & Answers
QUESTION:
Suppose that the waiting time for the first customer to enter a retail shop after . is a random variable with an exponential density function given by
\(f(y)=\left\{\begin{array}{ll}
\left(\frac{1}{\theta}\right) e^{-y / \theta}, & y>0, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
a Find the moment-generating function for .
b Use the answer from part (a) to find \(E(Y)\) and \(V(Y)\).
Equation Transcription:
Text Transcription:
f(y)=
(1 over theta)e^-y/theta, y>0
0, elsewhere.
E(Y)
V(Y)
ANSWER:
Solution 136E
Step1 of 3:
Let us consider a random variable Y it follows exponential distribution with density function:
Here our goal is:
a). We need to find the moment-generating function for Y .
b). We need to find E(Y ) and V (Y ).
Step2 of 3:
a).
We know that the probability distribution function of gamma distribution is:
Comparing this probability distribution func