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Feb
19
awarded  Good Answer
Feb
15
revised find the distribution of $Y=\lceil X/2\rceil$ while $X$ distribution is geometric?
added 1 character in body; edited title
Feb
15
answered find the distribution of $Y=\lceil X/2\rceil$ while $X$ distribution is geometric?
Jan
29
answered Cylindrical limits of integration for a particular triple integral
Jan
29
answered Seating arrangement probabilites
Jan
28
comment An integral with respect to the Haar measure on a unitary group
I used Mathematica. Define matrix $H$: hmat = Exp[I a/2] Table[WignerD[{1/2, m1, m2}, psi, th, phi], {m1, -1/2, 1/2}, {m2, -1/2, 1/2}]; Now define Haar measure weight measure[psi_, th_, phi_] := Abs[Sin[th]] 1/(4 (2 Pi)^3);. Check that it is normalized. Now evaluate Integrate[Det[DiagonalMatrix[{a1, a2}]-hmat.DiagonalMatrix[{d1, d2}].ConjugateTranspose[hmat]] measure[psi, th, phi], {th,0,2 Pi}, {psi,0,2 Pi}, {phi,0,2 Pi}, {a, 0, 2 Pi}], which gives $ \det(A-D) - \frac{1}{2} \left(A_{1,1}-A_{2,2}\right)\left(D_{1,1}-D_{2,2}\right)$.
Jan
28
comment An integral with respect to the Haar measure on a unitary group
If it helps, for $n=2$ the integral evaluates to $2 \det(A-D) - \left(A_{1,1}-A_{2,2}\right)\left(D_{1,1}-D_{2,2}\right)$.
Jan
26
comment Relation between convergence in distribution and in probability
Just to be clear $X \sim Y$ denotes $X \stackrel{\mathrm{law}}{=} Y$, i.e. equality in distribution (law).
Jan
24
awarded  Enlightened
Jan
24
awarded  Nice Answer
Jan
22
comment Deriving the Doob Meyer decomposition of a Sub Martingale using Ito's
The representation you obtained $X_t = \int_0^t \left(2 + 15 B_s^4\right) \mathrm{d}s + 6 \int_0^t B_s^5 \mathrm{d}B_s$ is correct.
Jan
19
revised Updating distribution with new samples
deleted 2 characters in body
Jan
19
awarded  Good Answer
Jan
6
awarded  Enlightened
Jan
6
awarded  Nice Answer
Jan
6
revised does the function $|\sin(x) |$ define a tempered distribution? if so compute the fourier transform
fixed formatting
Jan
2
comment Probability of a random point $(U_1,U_2, \cdots, U_n)$ with $U_j \sim \operatorname{Unif}(-1,1)$ being in unit sphere in $\mathbb{R}^n$
Please do, and also please accept it, perhaps waiting for a few days for constructive suggestions.
Jan
2
comment Probability of a random point $(U_1,U_2, \cdots, U_n)$ with $U_j \sim \operatorname{Unif}(-1,1)$ being in unit sphere in $\mathbb{R}^n$
Yes. Your solution is correct.
Jan
1
comment Probability and stuff
No kidding, but finding it rests with you. Happy New Year and best of luck in your endeavors.
Dec
31
comment Probability that rolling X dice with Y sides and summing the highest Z values is above some value k
The only way of doing it in R would be through simulations and simulation you can write in Python, R or many other freely available packages.