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In Exercises 5–20, conduct the hypothesis test and provide the test statistic and the P-value and /or critical value, and state the conclusion.
5. Testing a Slot Machine The author purchased a slot machine (Bally Model 809) and tested it by playing it 1197 times. There are 10 different categories of outcomes, including no win, win jackpot, win with three bells, and so on. When testing the claim that the observed outcomes agree with the expected frequencies, the author obtained a test statistic of χ2 = 8.185. Use a 0.05 significance level to test the claim that the actual outcomes agree with the expected frequencies. Does the slot machine appear to be
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- (c) Utilize Fubini's Theorem to demonstrate that E(X)= = (1- F(x))dx.arrow_forward(c) Describe the positive and negative parts of a random variable. How is the integral defined for a general random variable using these components?arrow_forward26. (a) Provide an example where X, X but E(X,) does not converge to E(X).arrow_forward
- (b) Demonstrate that if X and Y are independent, then it follows that E(XY) E(X)E(Y);arrow_forward(d) Under what conditions do we say that a random variable X is integrable, specifically when (i) X is a non-negative random variable and (ii) when X is a general random variable?arrow_forward29. State the Borel-Cantelli Lemmas without proof. What is the primary distinction between Lemma 1 and Lemma 2?arrow_forward
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