Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm having a bit of trouble wrapping my head around this one and would appreciate some guidance.

So we have two continuous (interdependent) random variables $X$ and $Y$, distributed uniformly on [0,$\theta$]. I'm looking for the joint density $f(y|X=x;\theta)$ where $\theta$ is a parameter. We also know that $\theta$ is distributed uniformly over [0,2] but not its value. I know that this is equal to the likelihood function $L(\theta;y|X=x)$ correct? I had no trouble calculating $f(y|x)$, but I'm not quite sure how to compute this function directly. There should be a way to apply some kind of Bayesian inference here, no?

This deals with auctions where $\theta$ is the previous winner's bid (fixed in the next round) if anyone is curious. The intuition is that knowing the previous winning bid $\theta$ causes the bidder in the next round to adjust how much he is willing to bid relative to his 'value' of the object.

share|improve this question
    
"...$f(y|X=x;\theta)$ where $\theta$ is a parameter" Doesn't make sense to me. I guess you actually meant that X and Y are uniformly distributed on $[0,\theta]$ ? –  leonbloy Jan 26 '13 at 22:38
    
Yes, sorry! I think you are correct. –  user59775 Jan 26 '13 at 22:41
    
At present, there is no clear question here. –  Did Jan 27 '13 at 9:51
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.