Sasha
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89/100 score
 Jul23 comment Is there one to one relation Positive definite(PD) matrix and PD function? @Creator I meant sphere, plane, their subsets, or some other domains. Jul23 comment Is there one to one relation Positive definite(PD) matrix and PD function? @Creator Do you require the purported function to have any specific domain, like $\mathbb{R}^2$ or $\mathbb{S}^2$? Jul23 comment Is there one to one relation Positive definite(PD) matrix and PD function? Any requirements at to the P.D. function domain? Jul15 comment What is $0^0$ equal to? @PedroTamaroff Search engines are not helpful sometimes. It is OK to post in my view, but once the duplicate is identified, it is polite to delete the question. Jul1 awarded Enlightened Jun30 awarded Nice Answer Jun9 reviewed Close compute standard basis in local rings Jun9 reviewed Close In a 30-60 right triangle the side opposite the 30 degree angle is half the length of the hypotenuse. Why? Jun9 reviewed Close Is there a formal definition for antiderivatives? Jun9 reviewed Close Convergence of sequence of function in norm. Jun8 comment Solving for n in the equation $\left ( \frac{1}{2} \right )^{n}+\left ( \frac{1}{4} \right )^{n}+\left ( \frac{3}{4} \right )^{n}=1$ No, $n \approx 1.7305073578576$. Jun5 comment Inside a circle, radius 1, 10 points are chosen. $X$- random variable that represents the distance from the rim of the circle to the closest point. Yours is the same as mine. In your case $n=10$ and the event $\{A\}$ is exactly $D > d$. Jun5 comment Maximum of a multivariable function The answer to this problem (the maximum of $f$ subject to this condition) can be expressed in algebraic numbers only (as a root of a polynomial of order 8). Are you sure there is no typo? Try Maximize[{y^2 - 2 z^2 + 2 x^2 y, 0 <= x <= 1 && 0 <= y <= 1 && 0 <= z <= 1 && x == z + y Sqrt[1 - y^2]}, {x, y, z}, Reals] // FullSimplify if you have access to Mathematica. Jun5 answered Inside a circle, radius 1, 10 points are chosen. $X$- random variable that represents the distance from the rim of the circle to the closest point. Jun5 revised The probability of more than $10$ people getting their own hat is no more than $1/100$ added 4 characters in body Jun2 revised Expectation of the min of two independent random variables? fixed typo in the text Jun2 comment PDF of a sum of exponential random variables It is called the law of total expectation. Indeed $f_Y(y) = \Pr(Y=y) = \mathbb{E}\left([Y=y]\right) = \mathbb{E}\left(\mathbb{E}\left([Y=y] \mid N\right) \right) = \mathbb{E}\left(f_{Y|N}\left(y\right) \right)$. May30 revised Infinite sum of reciprocals of pentagonal numbers deleted 2 characters in body May30 answered Infinite sum of reciprocals of pentagonal numbers May29 comment Joint probability distribution (over unit circle) By using $\{\sqrt{x^2+y^2} \leqslant u\} \equiv \{ -u \leqslant x \leqslant u, -\sqrt{u^2 - x^2} \leqslant y \leqslant \sqrt{u^2-x^2} \}$.