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U.S. Census Bureau estimates of the average number of persons per household in the United States for census years between 1850 and 2000 are shown in the following table. (These data are in the file perhouse on the companion website.)
a. Draw a scatterplot for the relationship between persons per household and year. Is the relationship linear or curvilinear? Is the association between persons per household and year positive or negative?
b. On your scatterplot, add a line that you believe fits the data pattern. Extend this line to the year 2010. On the basis of this line, estimate the number of persons per household in the United States in the year 2010.
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As in Problem 4 in §10.1, let X1, X2,... , be i.i.d. real random variables with E |X1| ∞. Let Sn := X1 +· · · + Xn . For n = 1, 2,... , let T-n := Sn/n. Let B-n be the smallest σ-algebra for which Sk are measurable for all k ≥ n. Show that {Tk, Bk..
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