Solution Found!
In Exercise 5.12, we were given the following joint
Chapter 5, Problem 30E(choose chapter or problem)
In Exercise 5.12, we were given the following joint probability density function for the random
variables \(Y_{1}\) and \(Y_{2}\), which were the proportions of two components in a sample from a mixture of insecticide:
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
2, & 0 \leq y_{1} \leq 1,0 \leq y_{2} \leq 1,0 \leq y_{1}+y_{2} \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
a Find \(P\left(Y_{1} \geq 1 / 2 \mid Y_{2} \leq 1 / 4\right)\).
b Find \(P\left(Y_{1} \geq 1 / 2 \mid Y_{2}=1 / 4\right)\).
Equation Transcription:
Text Transcription:
Y_1
Y_2
f(y_1,y_2)=
2, 0</=y_1</=y_2</=1,0</=y_1+y_2</=1,
0, elsewhere.
P(Y_1>/=1/2|Y_2</=1/4)
P(Y_1>/=1/2|Y_2=1/4)
Questions & Answers
QUESTION:
In Exercise 5.12, we were given the following joint probability density function for the random
variables \(Y_{1}\) and \(Y_{2}\), which were the proportions of two components in a sample from a mixture of insecticide:
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
2, & 0 \leq y_{1} \leq 1,0 \leq y_{2} \leq 1,0 \leq y_{1}+y_{2} \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
a Find \(P\left(Y_{1} \geq 1 / 2 \mid Y_{2} \leq 1 / 4\right)\).
b Find \(P\left(Y_{1} \geq 1 / 2 \mid Y_{2}=1 / 4\right)\).
Equation Transcription:
Text Transcription:
Y_1
Y_2
f(y_1,y_2)=
2, 0</=y_1</=y_2</=1,0</=y_1+y_2</=1,
0, elsewhere.
P(Y_1>/=1/2|Y_2</=1/4)
P(Y_1>/=1/2|Y_2=1/4)
ANSWER:
Step 1 of 2
a)
