BEPP 305 Lecture Notes - Lecture 2: Hot-Hand Fallacy, The Hockey News, Structural Break

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Statistics allow us to infer probabilities based on past observations. Sample- a list of observations: age of students in a class, age people start school, distance between philly and other cities. Statistic- a function of the sample: usually a real-valued function. Sample mean: sample x = {x1, x2, (cid:454)n: measu(cid:396)e of a (cid:862)t(cid:455)pi(cid:272)al o(cid:271)se(cid:396)(cid:448)atio(cid:374)(cid:863) Law of large numbers - under certain conditions, the average of a large sample gets very close to the mean of the. You thi(cid:374)k that a pla(cid:455)e(cid:396) is ha(cid:448)i(cid:374)g a (cid:862)good da(cid:455)(cid:863) Studies indicate that the success on free throws and field goal attempts is independent across shots. Independent draws (i. e. coin flips) have been rare in our adaptive e(cid:374)(cid:448)i(cid:396)o(cid:374)(cid:373)e(cid:374)t, so (cid:449)e (cid:272)a(cid:374)"t predict them accurately. Instead, we evolved to solve problems where persistence or anti-persistence was important i. e. if a p(cid:396)edato(cid:396) (cid:396)e(cid:272)e(cid:374)tl(cid:455) passed, (cid:455)ou"(cid:396)e u(cid:374)likel(cid:455) to (cid:373)eet a(cid:374)othe(cid:396); it"s safe to go (cid:374)o(cid:449)

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