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INTRODUCTION TO STATISTICAL ANALYSIS. LEARNING OBJECTIVES: After studying this chapter, a student should understand: notation used in statistics; how to represent variables in a mathematical form for statistical purposes; how to construct frequency distributions, histograms, and bar graphs;
1.For instance, an unbiased and consistent estimator was the MoM for the uniform distribution: ^ n;MoM = 2 x. We proved it was unbiased in 7.6, meaning it is correct in expectation. It converges to the true parameter (consistent) since the variance goes to 0.
2 2 12 2 22 1 11 2 2 2 2 2 1 2 2 2 12 2 12 Confidence Interval for and 11 Hypothesis Test Statistic: where numerator . . 1 and denominator . . 1 right left ss ss FF s F ss s df n df n σ σ σ σ • << • =≥ =−= −
1 ••• Master List of Formulas Chapter 1 IntroduCtIon and desCrIptIve statIstICs NONE. Chapter 2 FrequenCy dIstrIbutIons In tables and Graphs Σx (Frequency) Σx n (Relative frequency) Σx n × 100 (Relative percent) Chapter 3 summarIzInG data: Center tendenCy µ= Σx N (Population mean) M = Σx n (Sample mean) M Mn w n = Σ × Σ (Weighted sample mean) Chapter 4 summarIzInG data: varIabIlIty
pretability, using di!erent statistical learning methods. In general, as the ßexibil-ity of a method increases, its interpretability decreases. Other methods, such as the thin plate splines shown in Figures 2.5 and 2.6, are considerably more ßexible because they can generate a much wider range of possible shapes to estimatef .
Chapter 1 1. Method (c) is probably best, with (e) being the second best. 2. In 1936 only upper middle class and rich people had telephones. Almost all voters have telephones today. 3. No, these people must have been prominent to have their obituaries in the Times; as a result they were probably less likely to have died young than a randomly ...
The moment generating function of a discrete random variable X is de ned for all real values of t by. MX (t) = E etX = = x) X etxP(X. x. This is called the moment generating function because we can obtain the moments of X by successively di erentiating MX (t) wrt t and then evaluating at t = 0. 0 MX(0) = E[e0] = 1 = 0.
