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Critical Thinking. For Exercises 5-20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a)
19. California Smokers In the California Health Interview Survey, randomly selected adults are interviewed. One of the questions asks how many cigarettes are smoked per day, and results are listed below for 50 randomly selected respondents. How well do the results reflect the smoking behavior of California adults?
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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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