Solution Found!
Let (Y1, Y2) denote the coordinates of a point chosen at
Chapter 5, Problem 17E(choose chapter or problem)
Let \(\left(Y_{1}, Y_{2}\right)\) denote the coordinates of a point chosen at random inside a unit circle whose center is at the origin. That is, \(Y_{1} \text { and } Y_{2}\) have a joint density function given by
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
\frac{1}{\pi}, & y_{1}^{2}+y_{2}^{2} \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
Find \(P\left(Y_{1} \leq Y_{2}\right)\).
Equation Transcription:
Text Transcription:
(Y_1,Y_2)
Y_1 and Y_2
f(y_1,y_2)=
1 over pi, y_1^2+y_2^2</=1,
0, elsewhere.
P(Y_1</=Y_2)
Questions & Answers
QUESTION:
Let \(\left(Y_{1}, Y_{2}\right)\) denote the coordinates of a point chosen at random inside a unit circle whose center is at the origin. That is, \(Y_{1} \text { and } Y_{2}\) have a joint density function given by
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
\frac{1}{\pi}, & y_{1}^{2}+y_{2}^{2} \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
Find \(P\left(Y_{1} \leq Y_{2}\right)\).
Equation Transcription:
Text Transcription:
(Y_1,Y_2)
Y_1 and Y_2
f(y_1,y_2)=
1 over pi, y_1^2+y_2^2</=1,
0, elsewhere.
P(Y_1</=Y_2)
ANSWER:
Solution 17E
Step1 of 2:
Let us consider a random variables () denotes the coordinates of a point chosen at random inside a unit circle whose center is at the origin. Also we have joint density function of
:
We need to find