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 Yearling
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11h
comment Is the axiom of choice really all that important?
populist question.
11h
reviewed Approve Eigenvalues and eigenvectors for orthogonal projection
12h
reviewed Reject Diagonalization and $T(f(t))=f(t+1)$
15h
comment A short question about the convexity of a function
okay it seems above, it is not guaranteed to be greater than zero because $f^{''}(x)>0$, $r^{'}(f(x))<0$, and $r^{''}(f(x))>0$ and $f^{'}(x)^2>0$.
16h
comment A short question about the convexity of a function
Yes but concave or convex? I did this: $h=r(f(x))$ for $r=g^{-1}$ and $f=1-g$. Then $h^{''}(x)=r^{''}(f(x))f^{'}(x)^2+r^{'}(f(x))f^{''}(x)>0$, so $h$ is convex. Is what I did actually trivial? cannot $f(x)$ change the function from convex to concave?
17h
comment A short question about the convexity of a function
Jack, sorry it is probably a bit late but I am trying understand the conclusion of your answer and I am confused in the last parts. Until $(1)$, everything is okay. First, why should $(1)$ imply that if $h(x)$ in a small neighborhood of $1$ is convex, then $h(x)$ is convex on $[0,1]$? I understood $h(x)$ around $1$ is the same with $g$ around $0$. Then $g$ is concave around $0$, so $f=1-g$ is convex, which is fine. Then, $h=g^{-1}(f)$ is convex but how? Is it true that decreasing function of a convex function is convex? Could you please help me understand these two points? thanks in advance.
23h
reviewed Approve mensuration-Surfaces area and volumes
23h
revised Is the given binomial sum almost everywhere negative as $K\to\infty$?
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2d
awarded  Yearling
Apr
23
comment Random variable with infinite expectation
@did just a suggestion. I mean it is the choice of OP but there may be also other people who can appreciate other answers too, I would personally)
Apr
23
comment Random variable with infinite expectation
@did why dont you write it as an answer? dont you think that is seems ugly as a comment?
Apr
23
answered Negative binomial distribution pmf derivative
Apr
23
revised Econometrics/Statistics, variance and means
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Apr
23
comment Econometrics/Statistics, variance and means
I think first you must help us. what is the relation between $X$ and $Y$? what is 170? what is 10? kg? lb? cm?...
Apr
22
comment Variance of sample variance
Ok so this alone tells you that the variance of the estimator changes depending of the distribution of the random variable $X_i$. So the variance will not be the same for every $X_i$. If $n$ is assumed to be large enough, one can make use of central limit theorem and more than this is difficult to expect in my opinion.
Apr
22
revised Is the given binomial sum almost everywhere negative as $K\to\infty$?
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Apr
22
comment Variance of sample variance
It is equal to $E[X_i^4]-4E[X_i^3]\mu....$ so you already know how $X_i$ is distributed. The expectations are easy to calculate.
Apr
22
comment Variance of sample variance
you have the assumption of independence right? then what you did is correct and it is already simple and simplifies futher due to independence and linearity of expectation.
Apr
21
comment Find constant given two random variables and pdf
let me give you an important advice. Before doing everything. Just go to wikipedia (for any question you have now and will have in the future). Then type there simply "probability density function". In the page you find, search for the "properties" of a density function. Then think about how you must choose $K$ such that all conditions are satisfied.
Apr
21
comment Find constant given two random variables and pdf
@rightskewed this is what he must think and know himself.