Answered: Suppose Z is a discrete random variable…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....

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Suppose Z is a discrete random variable with the following probability distribution: P(Z = 0) = 0.1 P(Z = 1) = 0.3 P(Z = 2) = 0.4 P(Z = 3) = 0.2 What is the mode of Z?

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

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Step 1: Given information

Z is a discrete random variable with the following probability distribution:

$P left parenthesis Z equals 0 right parenthesis equals 0.1$

$P left parenthesis Z equals 1 right parenthesis equals 0.3$

$P left parenthesis Z equals 2 right parenthesis equals 0.4$

$P left parenthesis Z equals 3 right parenthesis equals 0.2$

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