Michael Hardy

Minneapolis

After doing nearly all the coursework for a Ph.D. in math, I then did all the coursework for a Ph.D. in statistics and completed that degree.
2h
revised Proving associativity of product of two formal sums $\sum_{n = 1}^{\infty} \frac{a_n}{n^x}$
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2h
answered Standard deviation formula confusion
2h
revised Standard deviation formula confusion
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2h
comment On non-existence of two independent random experiments on a same probability space
@User3101 : Just think of the problem of throwing a die. There are six possible outcomes, each with the same probability, $1/6$. If that choice were to determine two elements of $\{1,2,3,4,5,6\}$ chosen independently, that would mean that some one of those would give you the pair $(5,3)$, and that would happen one time out of $36$. But there is no outcome among $1,2,3,4,5,6$ that appears one time out of $36$. ${}\qquad{}$
1d
comment Bounds on $E[(f(X)-g(X))^2]$
If $X$ takes values in $\mathbb R^2$, then $f(X)$ and $g(X)$ could be the two separate scalar components, and for certain distributions of $X$ those are independent, and it's just as if you're looking for bounds on $\operatorname{E}((U-V)^2)$ for independent random variables $U,V$. If $X$ is real-valued, one can do similar things but I expect it takes somewhat more work. ${}\qquad{}$
1d
revised Bounds on $E[(f(X)-g(X))^2]$
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1d
revised $f(X)$ is uncountable and hence $X$ is uncountable.
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1d
revised Non-commutative noetherian integral domain-Ore condition
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1d
revised Pattern Inventory of Floating Pentagon
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1d
comment $f(X)$ is uncountable and hence $X$ is uncountable.
I changed "non constant" to "non-constant". In recent years I have so often encountered this usage, in which people write "non whatever" instead of either "non-whatever" or "nonwhatever", as if "non" were a word rather than a prefix, that I may some day start to suspect that this is not merely a typo and maybe some people think that is standard. ${}\qquad{}$
1d
revised $f(X)$ is uncountable and hence $X$ is uncountable.
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1d
revised Prove statement about relation of trace and eigenvalues
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1d
revised Dimensions of spaces over different fields
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1d
comment Dimensions of spaces over different fields
Your way of using MathJax is bizarre. I've cleaned it up. For example, I changed $\Bbb C$ 2 = $\{$ ${w \choose z}$:w,z$\in$ $\Bbb C$ $\}$ to $\Bbb C_2 = \{ {w\choose z}:w,z\in\Bbb C\}$. I also altered some notation, changing $(x_1,x_2,x_3,x_4,x_5)$ to $\{x_1,x_2,x_3,x_4,x_5\}$ since this apparently should be a set rather than a tuple. ${}\qquad{}$
1d
revised Dimensions of spaces over different fields
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1d
comment What is the difference between the heaviside distribution and the dirac delta distriubtion?
They are not different distributions. One could say the Dirac delta function is the density function and the Heaviside function is the cumulative distribution function, but of course the Dirac delta function isn't even really a function in the sense in which mathematicians usually define that term.
1d
revised an operator question
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1d
revised Question about inequality in linear algebra
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1d
revised Question for math purists: is the following proof related to harmonic series wrong?
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1d
comment How can a length of a shape be the same value as its area?
I would not say the value of a distance can equal the value of an area. I would say that the value of the number by which one multiplies one inch could be equal to the value of the number by which on another occasion one multiplies one acre. But the value of a distance I would take to be that which one could get by multiplying a number by a unit of distance. ${}\qquad{}$
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