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A routine exercise designed to test one's knowledge; often from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for such questions rather than complete answers.
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How to prove probability problem
I would approach it through a frequentist definition of probability, by showing that the set of events that count as D ∩ C has the same count as the set of events that count as D. That is P(D ∩ C) = …
1
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comparing one sample t-test, wilcoxon signed rank test, and sign test in a simulation
You can use the wilcoxon test and the sign test, you just create a second sample in which the null hypothesis value is zero (or whatever the H0 value for mu is) in each case. Then the differences are …