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Jun
26
awarded  Yearling
Jun
12
comment What is the best algorithm for finding a $g \in S_n$ which $a^g=b$ for given $a, b \in S_n$
Find the disjoint cycles in $a$ and $b$. Since you assume that they have the same cycle type, you can just match the cardinality of each cycle in $a$ and $b$.
Jun
11
revised Find the distribution of some random variable connected to Wiener Process. Please, check my solution.
added 2 characters in body
Jun
11
comment Find the distribution of some random variable connected to Wiener Process. Please, check my solution.
I think you might want to think of $D^2(W_t)$ as $\text{cov}(W_t, W_t)$ so you won't confuse yourself with the signs. Or better yet, think of $\text{cov}$ as the dot product. $D^2$ is just the square of the norm of the vector.
Jun
11
answered Find the distribution of some random variable connected to Wiener Process. Please, check my solution.
Jun
11
comment Relationship between sine and cosine in a circle
I would have thought this picture had been drawn on the board in his class already...
Jun
11
comment Find the distribution of some random variable connected to Wiener Process. Please, check my solution.
$W_7 - W_3$ has the same distribution as $W_4$, but it is not equal to $W_4$. (Otherwise $W_7$ would be completely determined by $W_3$ and $W_4$, which is NOT the case.)
Jun
11
comment Relationship between sine and cosine in a circle
I don't know if "in a circle" has any significance. May I guess $\sin(x)^2 + \cos(x)^2 = 1$?
Jun
11
comment Relationship between sine and cosine in a circle
There are a many answers to this. The simplest one I can think of right now is $\sin(x) = \cos\left(\frac{\pi}2 - x\right)$.
Jun
11
comment Will someone please explain multivariate normal distributions with a real-life example?
I can try to concoct one example. The GPS data at each time is a 2D random variable, which is assumed by many apps to be normally distributed.
Jun
11
answered Bernouli Trial Probability of Stopping After X Trials
Jun
11
revised Geometric Interpretation of Determinant of Transpose
added 406 characters in body
Jun
11
revised Geometric Interpretation of Determinant of Transpose
added 406 characters in body
Jun
10
asked Geometric Interpretation of Determinant of Transpose
Jun
10
revised How to encode matrices uniquely
added 54 characters in body
May
25
comment Prove that a function $f:X \to Y $ is injective if and only if $\forall x_1, x_2 \in X$ where $f(x_1) = f(x_2)$ implies that $x_1 = x_2$
Am I right to assume that "$x + 1$" is supposed to be "$x_1$"?
May
9
comment Function whose limit does not exist at all points
@moni94 Your function definition is not valid because the "last digit of the decimal representation" is not defined for every real number. (Take $1/7$ for example.)
May
9
comment How to find the eigenvectors.
@goods Well, you can arbitrarily pick one. The other one will be determined by your first choice.
May
9
answered How to find the eigenvectors.
May
9
comment How to find the eigenvectors.
@goods No. There can be infinitely many pairs that are still orthogonal to the other two.