Solution Found!
A production facility contains two machines that are used
Chapter 2, Problem 18E(choose chapter or problem)
A production facility contains two machines that are used to rework items that are initially defective. Let be the number of hours that the first machine is in use, and let
be the number of hours that the second machine is in use, on a randomly chosen day. Assume that
and
have joint probability density function given by
\(f(x)=\left\{\begin{array}{cc}
\frac{3}{2}\left(x^{2}+y^{2}\right) & 0<x<1 \text { and } 0<y<1 \\
0 & \text { otherwise }
\end{array}\right.
\)
a. What is the probability that both machines are in operation for more than half an hour?
b. Find the marginal probability density functions \(f_X(x)\) and \(f_Y(y)\).
c. Are and
independent? Explain.
Equation Transcription:
Text Transcription:
f(x)={_0 otherwise ^{3 over 2}(x^2+y^2) 0<x<1 and 0<y<1
f_X(x)
f_Y(y)
Questions & Answers
QUESTION:
A production facility contains two machines that are used to rework items that are initially defective. Let be the number of hours that the first machine is in use, and let
be the number of hours that the second machine is in use, on a randomly chosen day. Assume that
and
have joint probability density function given by
\(f(x)=\left\{\begin{array}{cc}
\frac{3}{2}\left(x^{2}+y^{2}\right) & 0<x<1 \text { and } 0<y<1 \\
0 & \text { otherwise }
\end{array}\right.
\)
a. What is the probability that both machines are in operation for more than half an hour?
b. Find the marginal probability density functions \(f_X(x)\) and \(f_Y(y)\).
c. Are and
independent? Explain.
Equation Transcription:
Text Transcription:
f(x)={_0 otherwise ^{3 over 2}(x^2+y^2) 0<x<1 and 0<y<1
f_X(x)
f_Y(y)
ANSWER:
Answer :
Step 1 of 4 :
Given, A production facility contains two machines that are used to rework items that are initially defective.
Let, X = number of hours that the first machine is in use and
Y = number of hours the second machine is in use
Let X and Y have the joint probability density function
