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Expected value of a roll of a fair die given that the number rolled is at least 4

I am trying to understand the solution to a probability problem, and I am having trouble understanding where some of the numbers are coming from. The textbook gives this definition for conditional ...
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What is the “Donkey Theorem”?

I was watching the Turkish version of Who Wants to Be a Millionaire? and they asked this question: What field is the Donkey Case (or I guess it can be translated as Donkey Theorem) related to? ...
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Simplifying Trace of a Matrix Expression ${\rm Tr} \left( (I- D^{-1} BA^2) B (I- D^{-1} BA^2)^T \right)$

Let $B$ be a symmetric invertible matrix and let $A$ be a diagonal matrix with non-zero entries on the main diagonal. I am trying to simplify the following expression \begin{align} {\rm Tr} \left( ...
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How is a dominant rational map well-defined?

I am slightly confused by the definition of a dominant rational map in Hartshorne, specifically because of a comment he makes about the equivalence relation. In Chapter 1.4, he defines a rational map ...
613 views

Reduce the payoff matrix using (weakly) dominated strategies

Below is the payoff matrix of a game. Use the principle of elimination of (weakly) dominated strategies to simplify the payoff matrix. What is the optimal solution of the game for the row player? ...
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Exponential equation without any sort of calcualtor

Is there a way i can solve the following equation only by using high school mathematics? $$4 \times2^x+3^x=5^x$$ i tried writing $5$ as $2+3$ but didn't get any result. After that i tried to divide ...
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How to convert a 2D coordinate system into a toroidal coordinate system?

I have a 100x100 square with each point having a node attached to it such that a node at point 0,99 is more similar to a node at point 0,0 than 0,95 lets say. The same can be said about the other axis....
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What are pullbacks of finite-coproduct injections along arbitrary morphisms?

I am studying a definition of an extensive category: An extensive category is a category $E$ with finite coproducts such that pullbacks of finite-coproduct injections along arbitrary morphisms exist ...
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When is a 5th degree polynomial with at least 1 non-real root solvable by radicals?

Let $f(X)$ be an irreducible polynomial of degree 5 with coefficents in the field of rational numbers $\mathbb{Q}$. Assume that $f$ has at least one non-real root in the complex field $\mathbb{C}$. ...