All Questions
1,659,234
questions
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Kurtosis of b(n,p) - binomial distribution
So I been at this for hours. I don’t know where my simplification is going wrong but here it is:
$\frac{n[(n-1)(n-2)(n-3)p^4 + 6(n-1)(n-2)p^3 +7(n-1)p^2 + p] - 4(n[(n-1)(n-2)p^3 +3(n-1)p^2 + p + 6(np)^...
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21
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Path independence in Complex Integration
I am reading this book called 'Complex Variables' by H.S. Kasana, in which there is proposition stated as follows:
Suppose that a function $f$ is continuous in a domain D. Then the following ...
- 157
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21
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Double-checking my formula derivation
The formula for the surface area of a right antiprism with regular n-gonal bases B isn't on the wikipedia page for antiprisms so I derived it myself. Based on the diagram below
I got that Surface ...
- 97
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1
answer
27
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Use $\,\varepsilon-\delta\,$ definition of limits to show that $\lim\limits_{(x,y)\to(-1,2)}\frac{x^3+y^3}{x^2+y^2}=\frac{7}{5}$
We need to show that for every $\varepsilon >0$ there exists a $\delta >0$ such that
$$\left\lvert\frac{x^3+y^3}{x^2+y^2}-\frac{7}{5}\right\rvert<\varepsilon $$
whenever
$$0<\sqrt{(x+1)^2+(...
- 107
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15
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Any two disjoint subsets in a family of subsets intersect, prove that any maximal such family of subsets must contain $2^{n-1}$ subsets
Here is the problem: Let $\mathcal{F}$ be a family of subsets of an $n$-element set $X$ with the property that any two members of $\mathcal{F}$ meet, i.e., $A \cap B \neq \emptyset$ for all $A, B \in \...
- 21
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14
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Let $f,g\in C[0,1]$ and $U= \{h\in C[0,1]:f(t)<h(t)<g (t),\forall t\in [0, 1]\}$ in $X= (C[0,1], \| .\|_{\infty} ).$ Is $U$ a ball in $X?$
Let $f,g: [0,1]\to\Bbb R$ be continuous and $f(t) < g (t)$ for all
$t\in [0,1].$ Consider the set
$$U= \{h\in C[0,1] : f (t) < h(t) < g (t) ,\text{ for } t\in [0, 1]\}$$
in the space $X= (C[0,...
- 3,065
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14
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multiplication in the ring of formal Laurent series
Let $F$ be a field and define the ring $F((x))$ of formal Laurent series with coefficients from $F$ by
$$
F((x))=\left.\left\{\,\sum_{n\geqslant N}^{\infty}a_nx^n\,\right|\,a_n\in F\text{ and }N\in\...
- 351
-1
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29
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Number of paths to go from (0,0) to (6,4), each step can only be one up or to the right, and no three consecutive steps in the same direction?
here is a question I encountered in a quant trading interview. I did not find a way to count cases with three consecutive steps that are not too messy. How to approach this problem? Any help would be ...
-1
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0
answers
19
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Locus of a circumcentre [closed]
A triangle is formed by the lines $x + y = 0$ , $x − y = 0$ and $lx − my = 1$.
If $l$ and $m$ are subjected to the condition $ l^2 +m^2 = 1$, then the locus of its circumcentre is
-1
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0
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23
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How to compute Contour Integral Numerically
So I am trying to compute the integral from $0$ to $a$ on the real axis, shown in the picture, for a function that is completely analytic on the upper half plane except at $E + i\epsilon$ where $\...
- 9
2
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17
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Projection onto a real subspace within a complex vector space
Given a complex vector space $V$, choose a finite set of vectors from $V$:
$$S = \{v_1, v_2, ..., v_n\}.$$
Now consider the following "real subspace" of V:
$$R = \{\sum_{i=1}^n a_i v_i: a_i \...
- 171
2
votes
0
answers
33
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A method of solving systems of linear equations in C.
It is known that a complex number $a + bi$ may be represented as a matrix in the form below:$$ \begin{bmatrix}
a & -b \\
b & a
\end{bmatrix} $$
Suppose that we have a system of linear ...
- 147
2
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14
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Continuity of $L_p$ norms
I am solving Exercise 3.21 of section 4 in Erhan Cinlar's book - Probability and Stochastics. The question is:
Fix a random variable $X$. Define $f(p)=\|X\|_p$ for $p\in[1,\infty]$. Show that the ...
- 33
2
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1
answer
29
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Sum of Repetends of Prime Reciprocals
Just a recreational mathematician here with a random question. All reciprocals of primes are periodic and there is some rational number that approximates them exactly up to their period. For example, $...
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25
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Solutions to this odd Diff Eq with an integral in it?
I’ve come to this unusual Diff Eq in a statistical physics problem. A real positive density function $\rho\left(r,v\right)$ is a function of two real positive variables $0\leq r<\infty$ and $0\leq ...
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