mathematics

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Chapter 3
Random
Variables

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Definition 3.1
Concept of a Random Variable
Section 3.1
Example: Two balls are drawn in succession without replacement from
an urn containing 4 red balls and 3 black balls. The random variable Y is
the number of red balls.

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Definition 3.2
Definition 3.3

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Definition 3.4
Section 3.2
Discrete Probability Distribution

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Definition 3.5
Example: If a car agency sells 50% of its inventory of a certain foreign
car equipped with side airbags, find a formula for the probability
distribution of the number of cars with side airbags among the next 4
cars sold by the agency.

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Figure 3.1 Probability mass
function plot

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Figure 3.2 Probability histogram

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Figure 3.3 Discrete cumulative
distribution function

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Figure 3.4 Typical density functions
Section 3.3
Continuous Probability Distributions

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Figure 3.5 P(a < X < b)

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Definition 3.6

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Definition 3.7

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Figure 3.6 Continuous cumulative
distribution function