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What is the rationale behind ROC curves?I am not sure how ROC curves work. I see that the X-Axis is the false positive rate while the Y axis is the true positive rate.1) I don't understand how for a given statistical learning model, you could have the true positive and false positive rate to vary from 0 to 1. Are you changing parameters in the model to make it so?2) What about true negatives and false negatives? How are these represented in the curve?
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Discrete Math logically equivalent?Show that ( p ∧ q ) ∨ ( ¬ p ∧ ¬ q ) ≡ p ↔ qHow would I go about doing this?Do I use a truth table or a more "algebraic" process?
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How is 1 2 n ≤ sin ( 1 n ) ≤ 1 n
Question about the square root of a non-negative quadratic function.For which values of x does this applyx2+2x+1=x+1
How to graph the line x - 2 y = 6 ?
Let's say for example these two:3n2n+3(−1)n+1−(−1)n2n((−1)n+1n)2
f : R 2 → R is continuous and f ( t , x ) < 0 holds for t x > 0 and f ( t , x ) > 0 holds for t x < 0I want to show, that x ( t ) = 0 is the only solution of x ′ = f ( t , x )You can say, that there is an solution, because f is continuous. By the intermediate value theorem exists ξ ∈ [ − a , a ], such that f ( t , ξ ) = 0. I only have to show, that x ( t ) = 0 is unique. How can I do that?
Give an example of a refinement in mathematical modeling with contextual explanation.
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