Statistics- Unlocking The Power Of Data
2nd Edition
ISBN: 9781119308843
Author: Lock
Publisher: WILEY
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Chapter 1.2, Problem 39E
a.
To determine
Identify the sample.
b.
To determine
Identify the population of interest.
c.
To determine
Identify a population to which the sample can be generalized.
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5. Let X be a positive random variable with finite variance, and let A = (0, 1).
Prove that
P(X AEX) 2 (1-A)² (EX)²
EX2
6. Let, for p = (0, 1), and xe R. X be a random variable defined as follows:
P(X=-x) = P(X = x)=p. P(X=0)= 1-2p.
Show that there is equality in Chebyshev's inequality for X.
This means that Chebyshev's inequality, in spite of being rather crude, cannot be
improved without additional assumptions.
4. Prove that, for any random variable X, the minimum of EIX-al is attained for
a = med (X).
Chapter 1 Solutions
Statistics- Unlocking The Power Of Data
Ch. 1.1 - Prob. 1ECh. 1.1 - For the situations described in Exercises 1.1 to...Ch. 1.1 - For the situations described in Exercises 1.1 to...Ch. 1.1 - For the situations described in Exercises 1.1 to...Ch. 1.1 - For the situations described in Exercises 1.1 to...Ch. 1.1 - For the situations described in Exercises 1.1 to...Ch. 1.1 - In Exercises 1.7 to 1.10, a relationship between...Ch. 1.1 - In Exercises 1.7 to 1.10, a relationship between...Ch. 1.1 - Prob. 9ECh. 1.1 - Prob. 10E
Ch. 1.1 - Student Survey Variables Data 1.1 introduced the...Ch. 1.1 - Countries of the World Information about the...Ch. 1.1 - Spider Sex Play Spiders regularly engage in spider...Ch. 1.1 - Hormones and Fish Fertility When women take birth...Ch. 1.1 - Fast-Twitch Muscles and Race Example 1.5 studied a...Ch. 1.1 - Rowing Solo Across the Atlantic Ocean On January...Ch. 1.1 - Largest Cities in the World Seven of the ten...Ch. 1.1 - Trans-Generational Effects of Diet Can experiences...Ch. 1.1 - Trans-Generational Effects of Environment In...Ch. 1.1 - Hookahs and Health Hookahs are waterpipes used for...Ch. 1.1 - Prob. 21ECh. 1.1 - Don’t Text While Studying! For the 2015 Intel...Ch. 1.1 - Prob. 23ECh. 1.1 - Prob. 24ECh. 1.1 - Prob. 25ECh. 1.1 - Prob. 26ECh. 1.1 - Prob. 27ECh. 1.2 - In Exercises 1.28 to 1.31, state whether the data...Ch. 1.2 - Prob. 29ECh. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Prob. 32ECh. 1.2 - Prob. 33ECh. 1.2 - Prob. 34ECh. 1.2 - Prob. 35ECh. 1.2 - In Exercises 1.36 to 1.39, a biased sampling...Ch. 1.2 - Prob. 37ECh. 1.2 - Prob. 38ECh. 1.2 - Prob. 39ECh. 1.2 - In Exercises 1.40 to 1.45, state whether or not...Ch. 1.2 - Prob. 41ECh. 1.2 - Prob. 42ECh. 1.2 - Prob. 43ECh. 1.2 - In Exercises 1.40 to 1.45, state whether or not...Ch. 1.2 - Prob. 45ECh. 1.2 - Prob. 46ECh. 1.2 - Prob. 47ECh. 1.2 - In Exercises 1.46 to 1.50, indicate whether we...Ch. 1.2 - Prob. 49ECh. 1.2 - Prob. 50ECh. 1.2 - Prob. 51ECh. 1.2 - Wearing a Uniform to Work The website fox6now.com...Ch. 1.2 - Prob. 53ECh. 1.2 - Prob. 54ECh. 1.2 - Prob. 55ECh. 1.2 - Prob. 56ECh. 1.2 - Prob. 57ECh. 1.2 - Prob. 58ECh. 1.2 - Prob. 59ECh. 1.2 - Prob. 60ECh. 1.2 - Prob. 61ECh. 1.2 - Prob. 62ECh. 1.2 - Prob. 63ECh. 1.2 - Interviewing the Film Crew on Hollywood Movies...Ch. 1.2 - Sampling Some Hardee’s Restaurants The Hardee’s...Ch. 1.3 - Prob. 66ECh. 1.3 - In Exercises 1.66 to 1.71, we give a headline that...Ch. 1.3 - Prob. 68ECh. 1.3 - Prob. 69ECh. 1.3 - In Exercises 1.66 to 1.71, we give a headline that...Ch. 1.3 - Prob. 71ECh. 1.3 - Exercises 1.72 to 1.77 describe an association...Ch. 1.3 - Prob. 73ECh. 1.3 - Prob. 74ECh. 1.3 - Prob. 75ECh. 1.3 - Exercises 1.72 to 1.77 describe an association...Ch. 1.3 - Prob. 77ECh. 1.3 - In Exercises 1.78 to 1.81, we describe data...Ch. 1.3 - Prob. 79ECh. 1.3 - Prob. 80ECh. 1.3 - Prob. 81ECh. 1.3 - Prob. 82ECh. 1.3 - Prob. 83ECh. 1.3 - Prob. 84ECh. 1.3 - Prob. 85ECh. 1.3 - Prob. 86ECh. 1.3 - Prob. 87ECh. 1.3 - Prob. 88ECh. 1.3 - Prob. 89ECh. 1.3 - Do Online Cat Videos Improve Mood? Exercise 1.59...Ch. 1.3 - Green Spaces Make Kids Smarter A recent article50...Ch. 1.3 - Prob. 92ECh. 1.3 - Sitting Is the New Smoking A 2014 headline reads...Ch. 1.3 - Late Night Eating It is well-known that lack of...Ch. 1.3 - To Spoon or Not to Spoon? Does cuddling after sex...Ch. 1.3 - Prob. 96ECh. 1.3 - Prob. 97ECh. 1.3 - Diet Cola and Weight Gain in Humans A study59...Ch. 1.3 - Prob. 99ECh. 1.3 - Urban Brains and Rural Brains A study published in...Ch. 1.3 - Prob. 101ECh. 1.3 - Prob. 102ECh. 1.3 - Prob. 103ECh. 1.3 - Do Children Need Sleep to Grow? About 60% of a...Ch. 1.3 - Prob. 105ECh. 1.3 - Prob. 106ECh. 1.3 - Prob. 107E
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- 8. Recall, from Sect. 2.16.4, the likelihood ratio statistic, Ln, which was defined as a product of independent, identically distributed random variables with mean 1 (under the so-called null hypothesis), and the, sometimes more convenient, log-likelihood, log L, which was a sum of independent, identically distributed random variables, which, however, do not have mean log 1 = 0. (a) Verify that the last claim is correct, by proving the more general statement, namely that, if Y is a non-negative random variable with finite mean, then E(log Y) log(EY). (b) Prove that, in fact, there is strict inequality: E(log Y) < log(EY), unless Y is degenerate. (c) Review the proof of Jensen's inequality, Theorem 5.1. Generalize with a glimpse on (b).arrow_forward3. Prove that, for any random variable X, the minimum of E(X - a)² is attained for a = EX. Provedarrow_forward7. Cantelli's inequality. Let X be a random variable with finite variance, o². (a) Prove that, for x ≥ 0, P(X EX2x)≤ 02 x² +0² 202 P(|X - EX2x)<≤ (b) Find X assuming two values where there is equality. (c) When is Cantelli's inequality better than Chebyshev's inequality? (d) Use Cantelli's inequality to show that med (X) - EX ≤ o√√3; recall, from Proposition 6.1, that an application of Chebyshev's inequality yields the bound o√√2. (e) Generalize Cantelli's inequality to moments of order r 1.arrow_forward
- The college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 13 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.arrow_forwardThe Honolulu Advertiser stated that in Honolulu there was an average of 659 burglaries per 400,000 households in a given year. In the Kohola Drive neighborhood there are 321 homes. Let r be the number of homes that will be burglarized in a year. Use the formula for Poisson distribution. What is the value of p, the probability of success, to four decimal places?arrow_forwardThe college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 13 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.arrow_forward
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