Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)

10th Edition

ISBN: 9780137538461

Author: Robert Hogg, Elliot Tanis

Publisher: PEARSON+

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Chapter 5.3, Problem 14E

Let X 1 , X 2 , X 3 be independent random variables that represent lifetimes (in hours) of three key components of a device. Say their respective distributions are exponential with means 1000, 1500, and 2000. Let Y be the minimum of X 1 , X 2 , X 3 and compute P ( Y > 1000 ) .

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 5.3, Problem 13E

Chapter 5.3, Problem 15E

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Chapter 5 Solutions

Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)

Ch. 5.1 - Let X have a geometric distribution with parameter...Ch. 5.1 - Suppose that X is a continuous random variable...Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Let X have a gamma distribution with =3 and =2....Ch. 5.1 - The pdf of X is f(x)=2x,0x1. (a) Find the cdf of...Ch. 5.1 - Prob. 7E Ch. 5.1 - Let X have a logistic distribution with pdf...Ch. 5.1 - A sum of $50000 is invested at a rate R, selected...Ch. 5.1 - The lifetime (in years) of a manufactured product...

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Let X 1 , X 2 , X 3 be independent random variables that represent lifetimes (in hours) of three key components of a device. Say their respective distributions are exponential with means 1000, 1500, and 2000. Let Y be the minimum of X 1 , X 2 , X 3 and compute P ( Y &gt; 1000 ) .

Solution Summary: The author calculates the value of P(Y>1000). All the three variables are exponentially distributed with the means 1000,1500and

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Chapter 5 Solutions

Let X 1 , X 2 , X 3 be independent random variables that represent lifetimes (in hours) of three key components of a device. Say their respective distributions are exponential with means 1000, 1500, and 2000. Let Y be the minimum of X 1 , X 2 , X 3 and compute P ( Y > 1000 ) .