-1 Sample Spaces and Events

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ch01 v1
Mas 291 - 2021, ch04.v1a

2-1 Sample Spaces and Events
2-1.3 Events

2-1.1 Random Experiments

Definition

2-1 Sample Spaces and Events

Definition

2-1 Sample Spaces and Events

2-1.2 Sample Spaces

Example 2-1

2-1 Sample Spaces and Events

Example 2-1 (continued)

2-1 Sample Spaces and Events

Example 2-2

2-1 Sample Spaces and Events

Example 2-2 (continued)

2-1 Sample Spaces and Events

Tree Diagrams

Sample spaces can also be described graphically with tree diagrams.

When a sample space can be constructed in several steps or stages, we can represent each of the n1 ways of completing the first step as a branch of a tree.
Each of the ways of completing the second step can be represented as n2 branches starting from the ends of the original branches, and so forth.

2-1 Sample Spaces and Events

Example 2-3

2-1 Sample Spaces and Events

Figure 2-5 Tree diagram for three messages.

2-1 Sample Spaces and Events

2-1.3 Events

Definition

2-1 Sample Spaces and Events

2-1.3 Events

2-1 Sample Spaces and Events

2-1.3 Events

Example 2-6

2-1 Sample Spaces and Events

Definition

2-1 Sample Spaces and Events

Venn Diagrams

Figure 2-8 Venn diagrams.
2.1.4 Counting Techniques
A printed circuit board has eight different locations in which a component can be placed. If four different components are to be placed on the board, how many different designs are possible?

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1-1 Statistics in Engineering

-1 Sample Spaces and Events

2-1 Sample Spaces and Events

2-1.1 Random Experiments

Definition

2-1 Sample Spaces and Events

2-1.2 Sample Spaces

Definition

2-1 Sample Spaces and Events

2-1.2 Sample Spaces

Example 2-1

2-1 Sample Spaces and Events

Example 2-1 (continued)

2-1 Sample Spaces and Events

Example 2-2

2-1 Sample Spaces and Events

Example 2-2 (continued)

2-1 Sample Spaces and Events

Tree Diagrams

2-1 Sample Spaces and Events

Example 2-3

2-1 Sample Spaces and Events

2-1 Sample Spaces and Events

2-1.3 Events

Definition

2-1 Sample Spaces and Events

2-1.3 Events

Basic Set Operations

2-1 Sample Spaces and Events

2-1.3 Events

Example 2-6

2-1 Sample Spaces and Events

Definition

2-1 Sample Spaces and Events

Venn Diagrams