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1. Show that the set R\Q of irrational numbers, with usual topology (relative topology from R), is topologically complete.
2. Define a complete metric for R\{0, 1} with usual (relative) topology.
3. Define a complete metric for the usual (relative) topology on R\Q.
4. (a) If (S, d) is a complete metric space, X is a Gδ subset of S, and for the relative topology on X, Y is a Gδ subset of X , show that Y is a Gδ in S.
(b) Prove the same for a general topological space S.
5. Show that the plane R2 is not a countable union of lines (a line is a set {(x, y): ax + by = c} where a and b are not both 0).
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random sampling from four treatments produced the following
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Identify the null hypothesis, alternative hypothesis, test statistic, Critical Values, conclusion about the null hypothesis, and final conclusion that addresses the original claim.
the distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 8.1 ounces
General Discrete Random Variable
Assume that Leo advertises "If it takes more than 30 minutes to get your pizza, you get it free". What percentage of his take-out pizzas will have to give away free?
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Each of the numbers 1 through 10 inclusive has been written on a separate piece of paper. The 10 pieces of paper have been placed in a hat. If one piece of paper is selected at random, with replacement, find the probability that the number selecte..
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