A community for students.
Here's the question you clicked on:
 0 viewing
UnkleRhaukus
 2 years ago
find \[\langle \theta \rangle \]
for \(0≤\theta≤\pi/2\)
UnkleRhaukus
 2 years ago
find \[\langle \theta \rangle \] for \(0≤\theta≤\pi/2\)

This Question is Closed

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\[\langle x\rangle=\int\limits_0^{\pi/2}\theta\cdot\rho(\theta)\cdot\text d\theta \]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.4whats \(\rho(\theta)\) ?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0probability density

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\[1=\int\limits_0^{\pi/2}\rho(\theta)\cdot\text d\theta\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0assuming a unifirm probability distribution \[\rho(\theta)=A\] \[\frac 1A=\int\limits_0^{\pi/2}\text d\theta\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\[\frac 1A=\theta_0^{\pi/2}=\frac\pi2\] \[A=\frac 2\pi\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0so, \[\langle x\rangle=\frac 2\pi\int\limits_0^{\pi/2}\theta\cdot\text d\theta\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\[=\frac 2\pi \frac{\theta^2}{2} _0^{\pi/2}\] \[=\frac 2\pi \frac{\left(\pi/2\right)^2}{2}\] \[=\frac\pi 4\]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.4nice, pdf was assumed or given? assuming it as uniform simplified it a lot.....

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0i probably should have stated uniform probability distribution in the question

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0so for \(0≤\theta≤2\pi\)\[\langle \theta \rangle =\pi\] the expected angle in a circle is 180°

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.4uniform pdf will always give you midpoint as expectation....
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.