Group members should begin by consulting an almanac, newspaper, magazine, or the Internet to find two graphs that show “intriguing” data changing from to year. In one graph, the data values should be increasing relatively steadily. In the second graph, the data values should be decreasing relatively steadily. For each graph selected, write a mathematical model that estimates the changing variable x years after the graph’s starting date. Then use each mathematical model to make starting date. Then use each mathematical model to make predictions about what might occur in the future. Are there circumstances that might affect the accuracy of the prediction? List some of these circumstances.
Group members should begin by consulting an almanac, newspaper, magazine, or the Internet to find two graphs that show “intriguing” data changing from to year. In one graph, the data values should be increasing relatively steadily. In the second graph, the data values should be decreasing relatively steadily. For each graph selected, write a mathematical model that estimates the changing variable x years after the graph’s starting date. Then use each mathematical model to make starting date. Then use each mathematical model to make predictions about what might occur in the future. Are there circumstances that might affect the accuracy of the prediction? List some of these circumstances.
Solution Summary: The author compares the mathematical model for increasing revenue of internet publishing and broadcasting with the estimated value obtained from it.
Group members should begin by consulting an almanac, newspaper, magazine, or the Internet to find two graphs that show “intriguing” data changing from to year. In one graph, the data values should be increasing relatively steadily. In the second graph, the data values should be decreasing relatively steadily. For each graph selected, write a mathematical model that estimates the changing variable x years after the graph’s starting date. Then use each mathematical model to make starting date. Then use each mathematical model to make predictions about what might occur in the future. Are there circumstances that might affect the accuracy of the prediction? List some of these circumstances.
1. Sketch the following sets and determine which are domains:
(a) |z−2+i| ≤ 1;
-
(c) Imz> 1;
(e) 0≤ arg z≤ л/4 (z ± 0);
Ans. (b), (c) are domains.
(b) |2z+3| > 4;
(d) Im z = 1;
-
(f) | z − 4| ≥ |z.
8. Suppose that the moments of the random variable X are constant, that is, suppose
that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.
9. The concentration function of a random variable X is defined as
Qx(h) = sup P(x ≤ X ≤x+h), h>0.
Show that, if X and Y are independent random variables, then
Qx+y (h) min{Qx(h). Qr (h)).
Chapter 1 Solutions
Pearson eText for Thinking Mathematically -- Instant Access (Pearson+)
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