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$begingroup$

Let $theta sim U(0,2pi)$, $phi = cot^-1fraccostheta + hsintheta$, $0 < h leq 1$, please prove that $phi sim U(0, pi)$.

probability probability-distributions

share|cite|improve this question

edited Mar 19 at 12:06

Mostafa Ayaz

18.2k31040

asked Mar 19 at 12:03

ZFZouZFZou

11

$endgroup$

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  $begingroup$
  Use the title to tell what the problem is about, no more no less. The "hard" adjective is relative and useless.
  $endgroup$
  – leonbloy
  Mar 19 at 12:07
  

  
  
  
  


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  $begingroup$
  Have you tried drawing the graph of $phi$ as a function of $theta$ (e.g. for $h = 1/2$)?
  $endgroup$
  – Vincent
  Mar 19 at 12:26
  
  

  
  
  
  

add a comment | 

0

1

$begingroup$

Let $theta sim U(0,2pi)$, $phi = cot^-1fraccostheta + hsintheta$, $0 < h leq 1$, please prove that $phi sim U(0, pi)$.

probability probability-distributions

share|cite|improve this question

edited Mar 19 at 12:06

Mostafa Ayaz

18.2k31040

asked Mar 19 at 12:03

ZFZouZFZou

11

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Use the title to tell what the problem is about, no more no less. The "hard" adjective is relative and useless.
  $endgroup$
  – leonbloy
  Mar 19 at 12:07
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Have you tried drawing the graph of $phi$ as a function of $theta$ (e.g. for $h = 1/2$)?
  $endgroup$
  – Vincent
  Mar 19 at 12:26
  
  

  
  
  
  

add a comment | 

$begingroup$

Let $theta sim U(0,2pi)$, $phi = cot^-1fraccostheta + hsintheta$, $0 < h leq 1$, please prove that $phi sim U(0, pi)$.

probability probability-distributions

share|cite|improve this question

edited Mar 19 at 12:06

Mostafa Ayaz

18.2k31040

asked Mar 19 at 12:03

ZFZouZFZou

11

$endgroup$

share|cite|improve this question

edited Mar 19 at 12:06

Mostafa Ayaz

18.2k31040

asked Mar 19 at 12:03

ZFZouZFZou

11

share|cite|improve this question

edited Mar 19 at 12:06

Mostafa Ayaz

18.2k31040

asked Mar 19 at 12:03

ZFZouZFZou

11

edited Mar 19 at 12:06

Mostafa Ayaz

18.2k31040

edited Mar 19 at 12:06

Mostafa Ayaz

18.2k31040

asked Mar 19 at 12:03

ZFZouZFZou

11

asked Mar 19 at 12:03

ZFZouZFZou

11