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Aug
18
comment selection of balls of three colors with restrictions
(1) is correct (2) all brown balls are identical so there is 1 way to select 2 brown balls.
Aug
18
comment Integrating unit impulse function
@Clayton this is using Stjeltjes interpretation of the integral, allowing to take care of discrete points with a weight...
Aug
18
comment Integrating unit impulse function
Look at en.wikipedia.org/wiki/Dirac_delta_function
Aug
18
comment Integrating unit impulse function
You likely mean $\delta(t) = 0$ for $t \ne 0$. Note that (A) follows from (B) with $f(t) \equiv 1 \forall t$.
Aug
11
comment Show that if λ is an eigenvalue of a projection matrix P, then λ = 1 or λ = 0
+1, short and elegant
Aug
11
comment How to show vectors are linearly independent?
@Kaster done, please look again...
Aug
11
comment How to show vectors are linearly independent?
@Kaster You're right, but this case is different since they are eigenvalues of the same matrix. I will change the answer in a sec
Aug
11
comment How to show vectors are linearly independent?
@Kaster I did not use the full definition, what I used is a direct consequence of the definition...
Aug
11
comment How to show vectors are linearly independent?
@Kaster yes. If $\vec{v}, \vec{w}$ are LD, so is any other collection of vectors with these included. For your case, let $a = 0, b = -2$ and $c = 1$ and note that $$a\vec{u} + b \vec{v} + c \vec{w} = \vec{0}.$$ The constants in the definition of LD cannot be all zero, but some of them can be zero at will.
Aug
11
comment What is CDF $F_X(x) $ and $F_Y(y)$?
@Math-fun thank you very much, appreciate it, totally overlooked
Aug
11
comment How to show vectors are linearly independent?
@Kaster not sure this is intended for me. Add the brotherkase tag if not. Certainly, $\vec{v}, \vec{w}$ are linearly dependent and suitable constant are easily found.
Aug
11
comment How to show vectors are linearly independent?
@brotherkase What does it mean for $\vec{u}, \vec{v}, \vec{w}$ to be linearly dependent? Use the definition to show the relationship in the answer for some non-zero real numbers $a$ and $b$. Then, compute $$A \vec{u} = A \left(a \vec{v} + b\vec{w}\right)$$ and simplify this expression using the relationship you posted in your answer.
Aug
11
comment Intersection of Collection of Sets
I don't think you mean $A \in S$ -- after all, $S$ is an interval, $A$ is a subset, i.e. $A \subseteq S$ but not $A \in S$...
Aug
9
comment How do I compute such theoretical expectations?
What is the structure of the graph on which the random walk is being performed?
Aug
9
comment Finding standrad deviation $\sigma$
did you check that $1/3$ of the cartons can be reserved fresh for $22+$ days?
Aug
9
comment Prove formally that if $\lim_{n\to+\infty} a_n = +\infty$ then $lim_{n\to+\infty}b_n = +\infty.$
Write down what it means formally when a sequence diverges and use the fact that bs are larger than the as.
Aug
7
comment Fourier transform of $e^{-at^2}= \frac{1}{\sqrt{2a}}e^{\frac{-w^2}{4a}}$
@CameronWilliams so what should be done when the same person is asking the same question again within 2 hours of each try?
Aug
7
comment terminology for a “forward flow” type of random digraph
@Emisor I think he means if $i<j$ then there will be an edge with probability $p$. He is working on random graphs...
Aug
6
comment The equivalence principle and experiments concerning it?
I don't think this is the place for debate questions either...
Aug
5
comment Path continuous but not continuous
What are your thoughts on the problem?