8,058 reputation
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bio website linkedin.com/in/gt6989b
location New York, NY
age 36
visits member for 3 years, 4 months
seen yesterday

Aug
28
comment Is$\frac{\sqrt{a}}{\sqrt{b}}$ the same as $\sqrt{\frac{a}{b}}$?
Yes, they are different, but where both are defined (i.e. on the intersection of domains) - the values will coincide.
May
14
comment Find the distribution of $X_1^2 + X_2^2$?
@user111548 Yes.
May
14
comment Find the distribution of $X_1^2 + X_2^2$?
@user111548 no. I meant that the mgf of $X$ and mgf of $X/\sigma$ are not the same thing.
May
5
comment Proving breath first traversal on graphs
@DrJonesYu Think about what $\textrm{Next}$ is at iteration $k$ -- this is a set of all vertices $x \in V$, such that for some $u \in V$, which is $k-1$ steps from $r$, there is an edge $(u,x)$. But that means $x$ is in the connected component of $r$.
May
5
comment Conditional CDF
@Someone i think so, made the edit
May
5
comment How prove this $ n = \frac {a^3 + 2b^3} {c^3 + 2d^3}. $ infinitely many special numbers
For (2), from your equation follows that $a^3$ is even, so $a$ is even, so $a = 2A$ and the equation becomes $$4A^3 + b^3 = 19 \cdot 53 (c^3 + 2d^3),$$ and $b$ and $c$ must have the same parity.
May
5
comment Evaluate $\frac{2}{4}\frac{2+\sqrt{2}}{4}\frac{2+\sqrt{2+\sqrt{2}}}{4}\cdots$
Moreover, it's easy to see it is an increasing sequence, you just need to show it is bounded above.
May
5
comment Evaluate $\frac{2}{4}\frac{2+\sqrt{2}}{4}\frac{2+\sqrt{2+\sqrt{2}}}{4}\cdots$
The only thing i can think about - prove that the sequence of terms is a Cauchy sequence. This only requires differences between successive terms.
May
5
comment Evaluate $\frac{2}{4}\frac{2+\sqrt{2}}{4}\frac{2+\sqrt{2+\sqrt{2}}}{4}\cdots$
Numerically, converges to about $0.405284735 \approx \ln(1.5)$
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
nice and elegant
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
They do, you just have to express $\cos \theta$ in terms of $a_x, a_y, b_x, b_y$ and do the arithmetic.
May
1
comment How to find the full Taylor expansion of the following:
@user88595 fixed...
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
Well, you claimed it's a proof -- before we show that, it's not really a proof, is it?
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
Well, if $\vec{a} = a_x \hat{i} + a_y \hat{j}$, by definition, $$\left| \vec{a} \right| = \vec{a} \cdot \vec{a} = a_x^2 + a_y^2.$$
May
1
comment How to find the full Taylor expansion of the following:
@Frumpy partial fractions should reduce denominator to degree 1
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
I don't understand why this is a proof of geometric and algebraic equivalence. Algebraically, you argued $$\vec{a} \cdot \vec{b} = a_x b_x + a_y b_y.$$ Geometrically, you argued that $$\vec{a} \cdot \vec{b} = \left| \vec{a} \right| \cdot \left| \vec{b} \right| \cos \theta = \sqrt{a_x^2 + a_y^2} \sqrt{b_x^2 + b_y^2} \cos \theta. $$ Why are they the same???
Apr
30
comment Ball Probability help
@user3335209 from (B) you found $\mathbb{P}[\text{same color}] = 14/45$. They must be either same or different, so $$\mathbb{P}[\text{same color}] + \mathbb{P}[\text{different color}] = 1$$
Apr
28
comment A linear growth model with immigration
@Danny yes, $o(h)$ includes any constant factor...
Apr
28
comment A linear growth model with immigration
@Danny $o(h)$ and $-o(h)$ is the same thing.
Apr
28
comment What does “Formulate the system of equations for a finite difference discretisation of the problem” mean?
What is meant by the question is, find the set of linear equations one would need to solve to get the numerical approximation to the problem you described via the method of finite differences.