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1. On R2 let d((x, y), (u, v)) := ((x - u)2 + (y - v)2)1/2 (usual metric), e(x, y) := |x - u|+ |y - v|. Show that e is a metric and metrizes the same topology as d.
2. For any topological space (X, T ) and set A ⊂ X , the boundary of A is defined by ∂ A := A\int A. Show that the boundary of A is closed and is the same as the boundary of X \ A. Show that for any two sets A and B in X,∂( A ∪ B) ⊂ ∂ A ∪ ∂ B. Give an example where ∂( A ∪ B) /= ∂ A ∪ ∂ B.
Develop a regression model that could be used to predict the final average in the course based on the first test grade. Predict the final average of a student who made an 83 on the first grade.
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6 are won by peace and 4 are won by queen and 2 end in a draw. they agree to play a tournament consisting of 3 games. Find the probability that: 2 games end in a row.
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