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:

$$d_k = \beta \tan(\theta_k)+\alpha.$$

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:

$$p(\theta_k\,\, |\,\, \alpha, \beta) = \frac{p(\alpha,\beta\,\,|\,\,\theta_k)\pi^{-1}}{C},$$

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.