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awarded  Autobiographer
Oct
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awarded  Nice Question
Sep
26
accepted For the covariance formula, how are subtraction and multiplication defined for real-valued random variables.
Sep
25
comment For the covariance formula, how are subtraction and multiplication defined for real-valued random variables.
Ok. But then it seems that if we actually want to compute the covariance, then we are back to talking about PDFs.
Sep
25
comment For the covariance formula, how are subtraction and multiplication defined for real-valued random variables.
Ok, so a real-valued random variable maps all possible 'outcomes' onto a real value. There is no arithmetic mapping between the two, because the set of all possible outcomes is just like an un-ordered list of things that can happen? And multiple outcomes can map to the same value? But the concept of outcomes is at least useful to us here, because it allows us to understand $X$ and $Y$ as measurements of the same outcome, but differing in kind?
Sep
25
comment For the covariance formula, how are subtraction and multiplication defined for real-valued random variables.
@Did Ok, I get that its a function, which wouldn't exclude it from being a CDF, but what kind of function is it? I don't understand this notation ω↦X(ω)Y(ω). What is ω and ↦ ?
Sep
25
comment For the covariance formula, how are subtraction and multiplication defined for real-valued random variables.
@Did ok, so a random variable is more like a cumulative distribution function (which is derived from a PDF)? How do you multiply two functions?
Sep
25
revised For the covariance formula, how are subtraction and multiplication defined for real-valued random variables.
edited title
Sep
25
comment For the covariance formula, how are subtraction and multiplication defined for real-valued random variables.
@Calvin, yeah, real-valued random variables are basically just PDFs, right? What is pointwise? I mean, how do you solve $X - E[X]$ and $XY$, for example. I guess you do some calculus?
Sep
25
asked For the covariance formula, how are subtraction and multiplication defined for real-valued random variables.
Sep
23
awarded  Popular Question
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awarded  Famous Question
Jan
25
comment Why is a linear autonomous system asymptotically stable iff for all eigenvalues $\lambda$ of $A$, $Re(\lambda) < 0$
Damn, unfortunately my knowledge of linear algebra ends at eigenvectors. In retrospect I probably should have mentioned that in the question.
Jan
25
asked Why is a linear autonomous system asymptotically stable iff for all eigenvalues $\lambda$ of $A$, $Re(\lambda) < 0$
Jan
11
revised Expected size of the connected component containing a randomly selected node
changed 'are' to 'that our'.
Jan
11
suggested approved edit on Expected size of the connected component containing a randomly selected node
Dec
30
awarded  Famous Question
Nov
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Aug
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accepted if $\mathbf x$ is sampled randomly from a hypercube on $R^n$, what is the probability density for $|\mathbf x| = d$
Jul
31
comment A point minimizing total great circle distance to a given set of points on a hemisphere
@Rahul yes, now that you point that out, and specifically on the hemisphere, if that helps. I believe that a hemisphere guarantees that the geometric median will be unique, whereas on the sphere there could be an infinite number of points.