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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
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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
May
13
awarded  Nice Answer
May
11
comment Expected Number of Coin Tosses to Get Five Consecutive Heads
@pushpen.paul I used Mathematica
May
11
awarded  Popular Question