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 Aug 20 asked Reference request for Heine-Borel theorem Aug 17 comment Justify an unbiased estimator is UMVUE @MichaelHardy possible. Biased mles can be corrected for the bias and will eventually become unbiased. The question is if there are mles which are not sufficient statistic but they are umvue. I don't believe that there exist such. Aug 16 comment Justify an unbiased estimator is UMVUE In principe, a function of every sufficient statistic can be UMVUE. However, It is not sufficient. There are MLEs (a function of the sufficient statistic) which are not UMVUE. The problem is that in such a case it is non-trivial to say if there exists indeed which is UMVUE. My best guess is that UMVUE, if it exists should be a function of sufficient statistic. Aug 16 comment Justify an unbiased estimator is UMVUE I havent checked if you derived correclty but if so, then you end up with the roots of a second order polinomial. It seems that the roots must be real because the last term in your equation is positive, i.e. multiply all terms by $-2/n$ and check again. Another thing is that the root is a function of $T$, the last term of you polinomial after normalization by $-2/n$. This suggests, but not proves that $T$ is indeed a sufficient statistic. Aug 16 comment Justify an unbiased estimator is UMVUE find the likelihood function then take the logarithm and then find the maximum with respect to the parameter. Write them down in your question as EDIT or ADDED or My work. Then I will tell you more. Aug 16 comment Justify an unbiased estimator is UMVUE can you write down the steps you followed to obtain $T$. Intuitively one can expect that the variance of $T$ needs to be less than both the sample mean or sample variance estimator. Aug 16 comment Distributions, PDFs, and Random Variables in Measure Theory $f_X$ is the Radon-Nykodym derivative of the probability measure $P$ with respect to a $\sigma-$finitite measure $\mu$, so $f_X$ must be the density function. the measure $\mu$ for the discrete case is the counting measure, so assigns a unit measure to the singletons. Aug 8 comment Two fundamental questions about convexity of a function (number2) @MichaelGrant you said that in your example that the saddle value was unique. which point is that? I cannot use the method of partial derivatives. Could you please let me know how we get the point in this case?thx. Aug 7 comment averaging of multiple curves for signal processing you can average the signals are you average the numbers. In Matlab: $V_1=V_2+V_3$, the sizes of the vectors must be the same. If the some of the signals are more important, then you may want to weight it differently before summing up. Aug 7 comment averaging of multiple curves for signal processing you can put the image here just. Go to edit and use the icon above which appears as an image. Aug 7 comment Why are these two sigma algebras independent? what is $P(E)\cap P(Q)$? Aug 7 comment averaging of multiple curves for signal processing you may want to give more details about your question. what average curve are you talking about. why not taking the average of all 5 curves? Aug 1 comment What does it mean to be $0.9-$Dimension? how about "what does it mean to be a non-integer dimension" Jul 26 comment What is the PMF of the Hamming weight of a multinomial random variable? I dont think that there is nicer version. Jul 26 revised Almost everywhere differentiable definition added 2 characters in body Jul 19 awarded Notable Question Jul 18 comment Minimizing a summation? This question is not informative. It is reduced to a kind of calculus level. If I was a student, I would first ask why do we take the square of the difference but not for example the 4th power?why do we subtract but not divide? etc. Jul 18 revised Minimizing a summation? edited tags Jul 18 comment How to distribute a cost in a normal distribution the usual way of doing what you are talking about is to randomly sample from a certain normal distribution. You only need to give the parameters and the number of samples you want to have. Thats all. Jul 17 comment Why do we use $\mathbb{R}$? Real numbers are not so important for engineering applications. In engineering applications, real numbers are always quantized. Btw, there is no enough memory to say even a single one, e.g. $\pi$.