# All Questions

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### Determine the number of equivalence relations on the set {1, 2, 3, 4}

Hi this was a question listed on my last proofs and conjectures midterm. It is similar to my previous post however this asks a different question which is throwing me off.. Do I simply list all ...
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### Finding a posterior distribution of an exponential distribution parameter theta

Suppose that $X_1, ... , X_n$ each have an exponential distribution with parameter $\theta$, and suppose that the prior for $\theta$ is an exponential distribution with parameter $\lambda$. Find the ...
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### How to solve age word problems?

Roy is now 4 years older than Erik and half of that amount older than Iris. If in 2 years, roy will be twice as old as Erik, then in 2 years what would be Roy's age multiplied by Iris's age? Is ...
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### Completely lost on this ODE

This is from Carmen Chicone's book on page 5, and I don't even know where to start. I haven't done differential equations in a while so this is really a problem for me. I'll accept any hints or ...
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### Finite Subgroups Of $GL(2,\mathbb{R})$

I have the following question: Is it true that every finite subgroup of odd order in $GL(2,\mathbb{R})$ is cyclic? Thanks!
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### Increasing length of closed spline (scaling)

I have a 2D closed spline and I need to increase its total length by a factor k, without changing its curvature, basically scaling. If this spline was a circle, I ...
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### Directional derivatives of $f \mapsto \max f$

Consider the functional $\Psi \colon C^{0}([0,1]) \to \mathbb R$ defined by $$\Psi(f):=\max_{x \in [0,1]} f(x)$$ Find the directional derivative (if it exists) in the generic point $f$ in the ...
I understand the derivative as a limiting process, and I understand that $$f^{\prime}(a)=\lim_{h \to0}\frac{f(a+h)-f(a)}{h} \tag{1}$$ But I'm slightly confused about this property that the ...