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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 How to check hypothesis in statistical data?
I just learned that the homework tag has been banned. Unfortunately, I cannot edit my comment. So just ignore this part.
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. Btw: If this is homework, please add the respective tag.
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 $Y$.
Aug
2
revised Entropy of the product of two random variables
deleted 364 characters in body
Aug
2
comment Decomposition of $a\sin(\varphi t)+b\sin(\vartheta t)$ into AM and carrier
This is a very neat trick. However, I don't see how this helps me to decompose it into a single carrier and AM. With your trick, I get two of them. $\left(a+b\right)\cos\left(\frac{ \varphi-\vartheta}{2}t\right)\sin\left(\frac{ \varphi+\vartheta}{2}t\right)+\left(a-b\right)\sin\left(\frac{ \varphi-\vartheta}{2}t\right)\cos\left(\frac{ \varphi+\vartheta}{2}t\right)$