Intro Stats
4th Edition
ISBN: 9780321826275
Author: Richard D. De Veaux
Publisher: PEARSON
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Chapter 12.1, Problem 1JC
One common proposal for beating the lottery is to note which numbers have come up lately, eliminate those from consideration, and bet on numbers that have not come up for a long time. Proponents of this method argue that in the long run, every number should be selected equally often, so those that haven’t come up are due. Explain why this is faulty reasoning.
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1 for all k, and set o
(ii) Let X1, X2,
that P(Xkb) =
x > 0.
Xn be independent random variables with mean 0, suppose
=
and
Var Xk. Then, for
0x) ≤2 exp-tx+121
Στ
k=1
Lemma 1.1 Suppose that g is a non-negative, non-decreasing function such that
E g(X) 0. Then,
E g(|X|)
P(|X|> x) ≤
g(x)
Proof of this Theorem
Theorem 1.2 (i) Suppose that P(|X| ≤ b) = 1 for some b > 0, that E X = 0, and
set Var X = o². Then, for 0 0,
P(X > x) ≤ e−1x+1²²,
P(|X|> x) ≤ 2e−x+1² 0²
Chapter 12 Solutions
Intro Stats
Ch. 12.1 - One common proposal for beating the lottery is to...Ch. 12.3 - Prob. 2JCCh. 12 - Flipping a coin Flipping a fair coin is said to...Ch. 12 - Dice Rolling a fair six-sided die is supposed to...Ch. 12 - Flipping a coin II Your friend says: I flipped...Ch. 12 - Dice II After rolling doubles on a pair of dice...Ch. 12 - Wardrobe In your dresser are five blue shirts,...Ch. 12 - Prob. 6ECh. 12 - Prob. 7ECh. 12 - Prob. 8E
Ch. 12 - Sample spaces For each of the following, list the...Ch. 12 - Sample spaces II For each of the following, list...Ch. 12 - Prob. 11ECh. 12 - Rain The weather reporter on TV makes predictions...Ch. 12 - Winter Comment on the following quotation: What I...Ch. 12 - Snow After an unusually dry autumn, a radio...Ch. 12 - Prob. 15ECh. 12 - Prob. 16ECh. 12 - Auto insurance Insurance companies collect annual...Ch. 12 - Prob. 18ECh. 12 - Prob. 19ECh. 12 - Prob. 20ECh. 12 - Electronics Suppose that 46% of families living in...Ch. 12 - Homes Funding for many schools comes from taxes...Ch. 12 - Prob. 23ECh. 12 - Lefties Although its hard to be definitive in...Ch. 12 - Prob. 25ECh. 12 - Prob. 26ECh. 12 - Car repairs A consumer organization estimates that...Ch. 12 - Stats projects In a large Introductory statistics...Ch. 12 - Prob. 29ECh. 12 - Prob. 30ECh. 12 - Prob. 31ECh. 12 - Prob. 32ECh. 12 - 33. Energy 2011 A Gallup Poll in March 2011 asked...Ch. 12 - Prob. 34ECh. 12 - Prob. 35ECh. 12 - Prob. 36ECh. 12 - Prob. 37ECh. 12 - Prob. 38ECh. 12 - Prob. 39ECh. 12 - Blood The American Red Cross says that about 45%...Ch. 12 - Prob. 41ECh. 12 - Prob. 42ECh. 12 - Prob. 43ECh. 12 - Prob. 44ECh. 12 - Prob. 45ECh. 12 - The train To get to work, a commuter must cross...Ch. 12 - Prob. 47ECh. 12 - 48. Religion Census reports for a city indicate...Ch. 12 - Prob. 49ECh. 12 - Pepsi For a sales promotion, the manufacturer...Ch. 12 - 9/11? On September 11, 2002, the first anniversary...Ch. 12 - Prob. 52E
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