# All Questions

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### Universal hashing (bijection) with multiplication

I came across this question while thinking about a CS problem: Given a set $S = [a,b]$ , and a string $x \in S^{n}, x = r_1r_2 \cdots r_n$, under what conditions is $H(x) = r_1 * r_2 * \cdots * r_n$ ...
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### response impulse function

my question is related to time series modeling in signal form,i have such question,suppose we have time series data $y_1........y_n$,how can we represent in impulse response form?as i ...
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### Bird's Probabilities!!!

Please, could somebody help me to figure this exercise? You collect data on the wing lengths (Yi) of 50 bald eagles in one sample. The average wing length (Y sample average) is 89 cm and the ...
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### Calculation of gross salary from net

Assume the gross salary is $150,000$ monthly & tax brackets are as follows: $01 – 5,000 = 0$% Tax $5,001 – 12,500= 2$% Tax $12,501 – 100,000 = 10$% Tax More than $100,000 = 20$% Tax Now if we ...
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### Why must a finite symmetry group be discrete?

I'm having trouble justifying why a finite symmetry group is discrete. Can someone help?
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### Combinations of unequal probabilities

I want to find the probability that at least 6 people will attend an event given that n people are invited. However there's a different (independent) probability, Pn, for each person. Is there some ...
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### Determining slope of line relative to a maximum

In the following scientific report (Seismic Q estimation), a mathematical procedure of linear curve-fitting is described in words. The authors state: The stratigraphic effects are minimized by ...
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### Normalize data with large spread in values.

I'm currently trying to rank a set of data. The issue is that my initial rank comes from a search on google and the returning result set. The spread in values is ranging from 33 all the way up ...
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### Statistics - Interval Estimation - Proof

Please tell me how to start on this proof or give me some kind of hint. Please click on this link to see the question Show that if $X_1,X_2,\dots,X_n$ denotes an iid sample from $N(\mu,\sigma^2)$ ...
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### Markov Process with Stationary Distribution

I have the following problem: If I have a markov process with stationary distribution. The state space for the MP is integers. I also know that $P_{i,j}>0$ for all i and j. It is also given that ...
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### Discrete maths proposition, proof for multiplication

i have this multiplication table for ℤ5, ...
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### Definition of normal subgroup vs normal operator

Why is a normal operator defined as T such that $T^*T=TT^*$ rather than as an element in some normal subgroup N, i.e. $N = \{n| n\in G, gng^{-1}\in N\}$. Is the idea that a normal operator is "normal" ...
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### Composition of Injective and Surjective maps?

Consider a composite $f \circ g(x) = f(g(x))$ of two maps $X \xrightarrow{g} Y \xrightarrow{f} Z$. If $f$ is injective and $g$ is surjective, what is the results of the composition $f \circ g$? [or ...
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### Fermat's Little Theorem question?

For the statements, $x\equiv 4\pmod 5$ and $x\equiv 14 \pmod {15}$; What are the 3rd smallest positive integers for both statements?
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### Which definitions of builder notation exist for multiset theory?

Interesting cases would be $A=[1,1], B=[2]$ $[(a,b) \mid a \in A \wedge b \in B] = [(1,2),(1,2)]$ ? or $C=[1,2,3]$ $[x \mid c \in C \wedge x = c \mod 2] = [1,0,1]$ ? The only kind of informal ...
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### Convergence properties of nets and filterbases

Suppose $\mathcal{B}$ is a filterbase in $X$. If for each $B \in \mathcal{B}$, we have $x_B \in X$, then $\lambda: \mathcal{B} \rightarrow X$ such that $B \mapsto x_B$ is a net in $X$. Show that ...
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### Complex Potential of a Vortex in a Horizontal Strip

There is fluid in between two boundaries $\operatorname{Im} z = a$ and $\operatorname{Im} z = -a$, with a vortex of strength $Q$ at the origin. I need to find the complex potential using method of ...
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### Is $\{x\in\mathbb{R}^4: x\ge 0, \, x_1x_2+x_3x_4\ge\alpha\}$ convex?

Is $\{x\in\mathbb{R}^4: x\ge 0\, \mbox{ and }\, x_1x_2+x_3x_4\ge\alpha\}$, for $\alpha>0$, a convex set? A related question is this one: Is $f(x_1,x_2)=x_1x_2$, with $x_1,x_2 \in \mathbb{R}_+$, a ...
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### Least Squares Approx.

If I was using a least squares approximation of the form $y = A_1 + A_2\sin(wx) + A_3\cos(wx)$, would you be minimising the function $\sum_{i=0}^n (y_i - (A_1 + A_2\sin(wx) + A_3\cos(wx))^2$ ? I've ...
154 views

### Derivative of B-Spline curve

Using the notation in the book by Piegl, when I have to compute the derivative of a B-Spline curve, I write $\sum_{i=0}^n N_{i,p}P_i$ on the knot vector ...
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### non convex optimisation

\begin{eqnarray} {\textbf{maximise}} \hspace{2mm} Ar^{-(a+b)} + Br^{-(a+b+c)}-C \nonumber \end{eqnarray} such that, \begin{eqnarray} c= l(h-m_{0}) \nonumber\\ m_{1} \leq h \leq m_{2} \nonumber\\ ...
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### Calender Questions empirical or classical probability?

Questions like what is probability for monday to occur on year 2016 , i am confused wether such calender based questions are empirical (experimental) or Classical Probability. My teacher says that ...
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### Statistical variable transformation

i'm preparing my statistics exam and I dont know how to solve the following exercice: Let X be a Statistical variable having the following values: $x_1$,$x_1$,...$x_r$. It is known that ...
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### Expression Writing: Random variable inside bayesian (Notation)

What is the best, most clear way to denote this example. Event A: outcomes (0,1). P(C)=P(B), if A=1 P(C) = 0, if A=0 Which one is best 1) P(C) = P(B|A=1), A: indicator random variable 2) P(C) ...
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### probability marbles and coins

please help me get started on this question An urn contains 3 Red and 4 White marbles. A fair coin is flipped. If the flip is Heads then 1 Red and 2 White marbles are added to the urn. On the other ...
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### The support function of two sets are equal iff the sets are equal

I am not sure how to approach this question from Boyd. How to show that the support function of two sets $A$ and $B$ are equal iff $A=B$. The support function for a set $A$ is defined as ...
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### Other inverse binomial

An urn contains $x$ balls. We know that $p\%$ are red and $(1-p)\%$ are blue. We draw without replacement $n$ balls and get $n_1$ red balls. What is the probability that $x=k$ ? Same question if we ...
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### Rolling 5, 6 sided dice where top 3 equal 15. How many rolls? How in Recursion?

Let's say that I have 5 (n), 6-sided (d) normal dice. How would I figure out how many possible rolls there are, where the top 3 (k) numbers rolled, equal 15 (t)? How would I do this using recursion ...
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### parabola in homogeneous coordinates

So if I have the parabola Y = X^2, how do I go about representing this homogeneously? I know I can parameterize it as F(t) = (t, t^2), but then what? The reason I ask is because I have a 3*3 matrix ...
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### Show that interval is an event.

Let $\Omega =[0,1]$and we know that sets $[0,x]$, $0≤x≤1$ are events. Show using the properties of event space (sigma-algebra) that $(1/2,2/3)$ is also an event. I just started to study probability ...
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### Whether this set is convex or not?

Consider the closed disk of radius 1 at the origin. Let it be called set S. Now is the set $S'=S\setminus \{(1,0),(0,1)\}$ convex? I feel like it is convex but I am not sure how to prove. It basically ...
Given that point $P$ outside plane $\alpha$. Plane $\beta$ is a plane that contained point $P$ and perpendicular to one of the line in plane $\alpha$. If line $l$ is the intersection line between ...