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formulas - i FORMULA SHEET C E 398 Fall 2010 Please note...

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i FORMULA SHEET - CE 398 Fall 2010 Please note: You may not need all the formula on this sheet. Basic Probability Formula: p(S) = n(S)/n(U) Application of Set Theory to Probability: p(A u B) = p(A) + p(B) p(A n B) Mutually Exclusive Events: p(A u B) = p(A) + p(B) Non-mutually Exclusive Events: p(A u B) = p(A) + p(B) p(A n B) Statistically Independent Events: p(A n B) = p(A) * p(B) Statistically Dependent Events: p(A n B) = p(A) * p(B/A) Complementary Events: p(A) + p(A’) = 1 Expected Value (Discrete Distributions) Note: Specifically, for the Binomial distribution, expected value = n p Expected Value (Continuous Distributions) dx x f a X p a ) ( ) ( dx x f b X p b ) ( ) ( dx x f c X p c ) ( ) ( dx x f b X a p b a ) ( ) ( ] ) ( * [ ) ( 1 n i i i x f x X E dx x f x X E ) ( * ) (
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ii Lower-tailed 1-sided hypothesis tests H 0 : θ a H 1 : θ < a Upper-tailed 1-sided hypothesis tests H 0 : θ a H 1 : θ > a 2-tailed hypothesis tests H 0 : θ = a H 1 : θ a Calculated value of the test statistic: n x Z / *
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iii Question or Problem Define the claim under investigation and the counterclaim Formulate your hypothesis in words
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