Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose we have a uniform random variable $X$ (continuous) in an interval of length one $[\gamma,\gamma+1]$ but we don't know $\gamma$. We just take one sample $x_1$.

What can we say about $\gamma$? Can we give an estimate of its value?

share|cite|improve this question

That $x_1-1\leqslant\gamma\leqslant x_1$. Estimated value: $\gamma=(x_1-\frac12)\pm\frac12$.

share|cite|improve this answer
That's it? Can we assign probabilities to the points in $\gamma=(x_1-\frac12)\pm\frac12$? – Ambesh Aug 8 '13 at 9:50
"That's it?" Obviously, nothing more can be deduced from one observation. "Can we assign probabilities to the points..." The question is unclear, you might want to explain. – Did Aug 8 '13 at 10:58
What I mean if it's more likely that $\gamma=x_1$ than $\gamma=x_1-1$. I somehow see that it looks more likely $\gamma=x_1$ and it becomes less likely as we move away. But it's just my intuition. – Ambesh Aug 8 '13 at 13:28
Wrong. If you must give one value, choose $\gamma=x_1-\frac12$. This is the value which minimizes the error (and any $\gamma=x_1-\delta$ with $0\lt\delta\lt1$ would be better than $\gamma=x_1$). – Did Aug 8 '13 at 13:36
Could you justify these statements? – Ambesh Aug 8 '13 at 18:57

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.