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hard calculus distribution in probability



The Next CEO of Stack OverflowProbability distribution for the sum of two variables (binomial and uniform) - Specify distributionFind a specific probability distributionDistribution of arcsin of a uniform random variableBeckmann distributionProve that two processes have the same lawPolar transformation of a probability distribution functionProbability that $sintheta cosphi < 0.999772$Proving normal distribution in Box MullerProbability density function of $X$ with a uniform distribution on a unit sphereDistribution of $|sin(Theta)|$ if $Theta$ is uniform on $(0,2pi)$ and arcsine distribution










0












$begingroup$


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










share|cite|improve this question











$endgroup$







  • 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
















0












$begingroup$


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










share|cite|improve this question











$endgroup$







  • 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














0












0








0


1



$begingroup$


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










share|cite|improve this question











$endgroup$




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















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Mar 19 at 12:06









Mostafa Ayaz

18.2k31040




18.2k31040










asked Mar 19 at 12:03









ZFZouZFZou

11




11







  • 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













  • 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








1




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




$begingroup$
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




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





$begingroup$
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











0






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