World Series. TheWorld Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919–1921 World Series, when it was a best of nine). From the document World Series History on the Baseball Almanac website, as of November 2013, the lengths of the World Series are as given in the following table.Number of gamesFrequencyRelative frequency4210.2005240.2296240.2297360.343Let X denote the number of games that it takes to complete a World Series, and let Y denote the number of games that it took to complete a randomly selected World Series from among those considered in the table.a. Determine the mean and standard deviation of the random variable Y . Interpret your results.b. Provide an estimate for the mean and standard deviation of the random variable X. Explain your reasoning.

a.The random variable X denotes the number of games that it takes to complete a World Series and the…

Answered: World Series. TheWorld Series in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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World Series. TheWorld Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919–1921 World Series, when it was a best of nine). From the document World Series History on the Baseball Almanac website, as of November 2013, the lengths of the World Series are as given in the following table.

Number of games	Frequency	Relative frequency
4	21	0.200
5	24	0.229
6	24	0.229
7	36	0.343

Let X denote the number of games that it takes to complete a World Series, and let Y denote the number of games that it took to complete a randomly selected World Series from among those considered in the table.
a. Determine the mean and standard deviation of the random variable Y . Interpret your results.
b. Provide an estimate for the mean and standard deviation of the random variable X. Explain your reasoning.

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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