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 Feb 9 comment Property of covariance of Normal random variable with an arbitrary function of that random variable I see. It was just sloppy notation. They meant the average gradient instead of the average partial derivative w.r.t. $x_j$. Thanks for the hint. Apr 24 comment Property of covariance of Normal random variable with an arbitrary function of that random variable I don't have much more context. I found this equation in the paper, thought it was pretty neat but then found out that it is wrong. Now I am curious what the correct form of the equation would be. Price's theorem looks nice, but I cannot connect it to the equation above. Apr 23 asked Property of covariance of Normal random variable with an arbitrary function of that random variable Dec 9 awarded Caucus Sep 1 awarded Yearling Aug 15 comment How to check hypothesis in statistical data? I think Eupraxis1981 sums it up pretty nicely. Aug 15 comment Transforming two independent variables, probability Unfortunately, I am only allowed to edit comments for 5 minutes. So it will have to stay a trick. I am sorry ... Aug 15 comment Transforming two independent variables, probability I remember that I read the usual trick before and I liked it. However, I totally forgot about it. But it is always nice to read it again ... +1. Aug 15 comment Transforming two independent variables, probability Ah, oops. Didn't know that. Thanks user21820. Aug 15 revised Transforming two independent variables, probability added 526 characters in body Aug 15 answered Transforming two independent variables, probability Aug 15 comment How to check hypothesis in statistical data? Are you sure, the problem is posed like this? If yes, than it is badly posed. First of all, hypotheses are about statistics which are computed from the data. For example, an hypothesis could be that the mean number of hotel rooms is $50$. You case sounds more like "What is the probability that a randomly drawn object has more than 30 rooms". If that is the case, it is badly posed as well since you only have a sample from the probability distribution, but not the distribution itself. These might be very different things. Aug 15 comment How to check hypothesis in statistical data? I think the problem is that your hypothesis is not an hypothesis, but a probability event. To compute its probability, you need an underlying probability distribution. There might be ways of getting that from your data but it seems to me that this is more complicated than what you want. Aug 15 comment Transforming two independent variables, probability Hi user160522, I don't know exactly what earned you two down votes without a single comment on it, but I guess it is mainly because you didn't say in the question why you are interested in that problem (is it homework for example? If yes add the homework tag) and what you have tried. Also, it is called cumulative distribution function. Please update your question. I, in the meantime, will give you an answer. Aug 4 revised Entropy of the product of two random variables added 63 characters in body Aug 4 revised Entropy of the product of two random variables added 1125 characters in body Aug 4 comment Entropy of the product of two random variables I see, it is actually not that hard to show. But I think this also gives us the means to given an answer. Aug 4 comment Entropy of the product of two random variables Can you supply a proof for $H[XY]\le H[X]+H[Y]$? I immediately believe that the joint entropy is lower than the sum of the marginal entropies $H[X, Y]\le H[X]+H[Y]$, but for the matrix/vector product I am not so sure. Aug 3 comment Entropy of the product of two random variables But what does that prove? You just found an example for which it works. It might just not work for the majority of the other examples. In particular is $X$ is not a square matrix. Aug 2 comment Entropy of the product of two random variables My above comment only holds for binary $Y$.