(a) Explanation Given info: The random variable X has an adequate approximation of an exponential distribution with θ = 2 . Calculation: Exponential Distribution: A random variable X is said to follow Exponential distribution if the density function of X is, f ( x ) = 1 θ e − x θ , ( x > 0 , θ > 0 ) . Where the mean is μ = θ and the standard deviation is σ = θ . Here, θ = 2 . Thus, μ = θ = 2 . Moreover, as σ = θ , thus, σ = 2 . Now, 3 standard deviations from μ is μ ± 3 σ . μ ± 3 σ = 2 ± ( 3 × 2 ) = 2 ± 6 = ( − 4 , 8 ) (b) To determine To find: The probability that X assumes a value less than 2 standard deviations from μ . (c) To determine To find: The probability that X assumes a value within half a standard deviation from μ .

Statistics for Business and Economics (13th Edition)

13th Edition

ISBN: 9780134506593

Author: James T. McClave, P. George Benson, Terry Sincich

Publisher: PEARSON

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Chapter 4.8, Problem 4.138LM

(a)

To determine

To find: The probability that X assumes a value more than 3 standard deviations from μ .

(b)

To determine

To find: The probability that X assumes a value less than 2 standard deviations from μ .

(c)

To determine

To find: The probability that X assumes a value within half a standard deviation from μ .

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Chapter 4.8, Problem 4.137LM

Chapter 4.8, Problem 4.7AE

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Spam filters are built on principles similar to those used in logistic regression. We fit a probability that each message is spam or not spam. We have several variables for each email. Here are a few: to_multiple=1 if there are multiple recipients, winner=1 if the word 'winner' appears in the subject line, format=1 if the email is poorly formatted, re_subj=1 if "re" appears in the subject line. A logistic model was fit to a dataset with the following output: Estimate SE Z Pr(>|Z|) (Intercept) -0.8161 0.086 -9.4895 0 to_multiple -2.5651 0.3052 -8.4047 0 winner 1.5801 0.3156 5.0067 0 format -0.1528 0.1136 -1.3451 0.1786 re_subj -2.8401 0.363 -7.824 0 (a) Write down the model using the coefficients from the model fit.log_odds(spam) = -0.8161 + -2.5651 + to_multiple + 1.5801 winner + -0.1528 format + -2.8401 re_subj(b) Suppose we have an observation where to_multiple=0, winner=1, format=0, and re_subj=0. What is the predicted probability that this message is spam?…

Chapter 4 Solutions

Statistics for Business and Economics (13th Edition)

Ch. 4.1 - Types of random variables. Which of the following...Ch. 4.1 - Types of finance random variables. Security...Ch. 4.1 - NHTSA crash tests. Refer to the National Highway...Ch. 4.1 - Customers in line at a Subway shop. The number of...Ch. 4.1 - Executive pay. Refer to Glassdoor Economic...Ch. 4.1 - Banking. Give an example of a discrete random...Ch. 4.1 - Economics. Give an example of a continuous random...Ch. 4.1 - Hotel management. Give an example of a discrete...Ch. 4.1 - Retailing. Give two examples of discrete random...Ch. 4.1 - Stock market. Give an example of a continuous...

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The probability that X assumes a value more than 3 standard deviations from μ .

Solution Summary: The author explains that the probability that X assumes a value more than 3 standard deviations from mu is 0.018316.

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To find: The probability that X assumes a value more than 3 standard deviations from μ .

To find: The probability that X assumes a value less than 2 standard deviations from μ .

To find: The probability that X assumes a value within half a standard deviation from μ .

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Chapter 4 Solutions