Bayesian probability: The lighthouse problem

[Niles]

Homework Statement

Hi all.

Please take a look at this problem: http://web.gps.caltech.edu/classes/ge193/practicals/practical3/Lighthouse.pdf

I am stuck at question 2 and 3. For question 1 I get the following:

<br /> d_k = \beta \tan(\theta_k)+\alpha.<br />

For question 2 and 3, I know I have to use Bayes' sentence for probability density functions (PDF's), so for question 2 I get:

<br /> p(\theta_k\,\, |\,\, \alpha, \beta) = \frac{p(\alpha,\beta\,\,|\,\,\theta_k)\pi^{-1}}{C},<br />

where C is some constant that normalizes the PDF and I have assumed that the prior probability on \theta_k is \pi^{-1} (I was told to do this).

Could you guys tell me, what the next step is?

Thanks in advance.


Niles.

 

[Avodyne]

You're not supposed to use Bayes' theorem for #2. The answer to #2 is given by the statement that the pulses are emitted at "random azimuths". This presumably means that \theta_k is uniformly distributed between 0 and 2\pi.

 

[Niles]

Thanks! I'll keep working on it from here.