Sasha
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 Jun 9 reviewed Close Is there a formal definition for antiderivatives? Jun 9 reviewed Close Convergence of sequence of function in norm. Jun 8 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, $n \approx 1.7305073578576$. Jun 5 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 $D > d$. Jun 5 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. Jun 5 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. Jun 5 revised The probability of more than $10$ people getting their own hat is no more than $1/100$ added 4 characters in body Jun 2 revised Expectation of the min of two independent random variables? fixed typo in the text Jun 2 comment PDF of a sum of exponential random variables It is called the law of total expectation. Indeed $f_Y(y) = \Pr(Y=y) = \mathbb{E}\left([Y=y]\right) = \mathbb{E}\left(\mathbb{E}\left([Y=y] \mid N\right) \right) = \mathbb{E}\left(f_{Y|N}\left(y\right) \right)$. May 30 revised Infinite sum of reciprocals of pentagonal numbers deleted 2 characters in body May 30 answered Infinite sum of reciprocals of pentagonal numbers May 29 comment Joint probability distribution (over unit circle) By using $\{\sqrt{x^2+y^2} \leqslant u\} \equiv \{ -u \leqslant x \leqslant u, -\sqrt{u^2 - x^2} \leqslant y \leqslant \sqrt{u^2-x^2} \}$. May 29 answered Joint probability distribution (over unit circle) May 29 revised Joint probability distribution (over unit circle) added 14 characters in body; edited title May 20 revised bound on expectation of a two-variable function under an independent distribution added 12 characters in body May 18 awarded Yearling May 14 comment How to find value of an unknown in matrix to make system of linear equations consistent Answering your direct question, yes echelon form row reduction would work as well. May 14 comment How to find value of an unknown in matrix to make system of linear equations consistent If you subtract the third row from the second row, you see that the resulting row of the matrix is identical to the first row of the matrix. Consistency would require that the resulting rhs vector element is the same as the first, i.e. $\lambda-5 = -3$, hence $\lambda = 2$. May 14 revised How to do integration by parts with brownian motion? added 15 characters in body May 13 awarded Enlightened