All Questions
0
votes
0answers
2 views
Expected number of Diamonds in a 5-card hands
What would be the correct answer for expected number of diamonds in a 5-card hands?
I am thinking as follow:
Let
$X_i = 1$ if the i-th card is diamond, or $0$ otherwise.
$X_i = (1 \times P($i-th ...
0
votes
0answers
8 views
How to know the difference among groups generated under the same words
i use words generated many groups in maple,
what are the common properties under the same words
how to know the difference among them
1
vote
0answers
11 views
Property of a euclidean map
Why an euclidean map defined onto a domain $R$, so a map $\delta\colon R\smallsetminus\{0\}\to\mathbb{N}$, satisfies $\delta(a)\leq\delta(ab)$ for every $a,b\in R\smallsetminus\{0\}$?
In some books, ...
0
votes
0answers
3 views
getting PDF from a given Moment Generating Function
if the moment generating function mgf of a random variable w is M(t)=(1-7t)-20
find the
i)pdf
ii)mean
iii)variance of w
0
votes
0answers
3 views
Number of Solutions to Diophantine Equation
$(a)$ Let $c < 2\pi$ be a positive real number. Show that
there are infinitely many integers $n$ such that the equation
$x^2 + y^2 + z^2 = n$
has at least $c\sqrt n$ integer solutions.
$(b)$ Find ...
0
votes
0answers
10 views
Computing the integral $ \lim\limits_{\epsilon\to 0} \int_{-2}^{0} \frac{e^{1/x(x+2)}}{x+1+i\epsilon} $
I got stuck when calculating of this expression
$$
\lim_{\epsilon\rightarrow 0} \int_{-2}^{0} \frac{e^{\frac{1}{x(x+2)}}}{x+1+i\epsilon}
$$
I will be grateful for the advice.
0
votes
0answers
8 views
0
votes
0answers
4 views
How many number of multiplications and additions are required for SVD
I have a matrix of dimension $m \times n$. We know that SVD is a powerful tool to decompose a rectangular matrix. A matrix can be decomposed as $A=U*S*V'.$ I want to know how many multiplications and ...
0
votes
0answers
8 views
If a subgroup has finite-intersection with a compact neighbourhood of $1$, then it is discrete?
At page 79 of Basic Number Theory by André Weil, there is an argument showing that a subgroup of a topological group is discrete,
because there is a compact neighbourhood of $1$ with finite ...
0
votes
0answers
7 views
difference between expected values of distributions
let us assume two distributions $p$ and $p'$ over the set of naturals $N$.
Is it true the following property?
$\sum_{n \in N} p(n) \cdot n \le \sum_{n \in N} p'(n) \cdot n$
IFF
for all $0 \le u ...
0
votes
0answers
5 views
Quadratic inequality with boundaries
Here is a very old high school exam question I am trying to solve (purely for interest only):
If $a,b,c$ are real numbers such that $-1 \le ax^2+bx+c \le 1$ for $-1 \le x \le 1$ prove that $-4 \le ...
0
votes
0answers
7 views
Prove that $F_{x^{n+1}} \sim 5^{\frac{x-1}{2}}F_{x^n}^x \forall x,n \geq 1$, holding either variable constant while the other goes to infinity
I noticed from looking at the prime factorizations of some Fibonacci numbers that all those with an index equal to a power of 5 divided that power of five, a property not guaranteed by the strong ...
2
votes
1answer
12 views
How can one tell if a sequence is well-defined; is the axiom of choice needed?
This question is in the context of the following exercise:
Let $X$ be a first countable topological space, let $A \subseteq X$, and let $x \in X$ with $x \in \overline{A}$. Then there exists a ...
0
votes
0answers
7 views
Complex Statistic Problem
This is my hardest statistics problem. Please help.
The data below shows the times in minutes taken by 160 tourists to climb Mt. Everest from the same point. If the mean time was 65.5 minutes, ...
1
vote
1answer
9 views
The generalized eigenvectors of linear operator $T$ span space $V$, why?
I'm studying about determinant and I have a problem understanding the following (Proposition 3.4):
The problems I have are highlighted with red rectangles. If anyone can, could you clarify these ...
