# AP Statistics Curriculum 2007 Prob Simul

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==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Probability Theory Through Simulation== | ==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Probability Theory Through Simulation== | ||

- | === | + | ===Motivation=== |

- | + | Many practical examples require probability computations of complex events. Such calculations may be carried out exactly, using the proper [[AP_Statistics_Curriculum_2007_Prob_Rules | probability rules]], or approximately using estimation or simulations. | |

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+ | [[Image:SOCR_EBook_Dinov_Probability_012908_Fig3.jpg|200px|thumbnail|right]] | ||

+ | A very simple example is the case of trying to estimate the area of a region, A, embedded in a square of size 1. The area of the region depends on the demarkation of its boundary, as a simple closed curve, as shown on the picture. This problem relates to the problem of computing the probability of the event A as a subset of the sample-space S - square of size 1. In other words, if we were to throw a dart at the square, S, what would be the chance that the dart land inside A (under certain conditions, e.g., the dart must land in S and each location of S is equally likely to be hit by the dart)? | ||

+ | |||

+ | This problem may be solved exactly by using integration, but an easier approximate solution would be throwing 100 darts at the board and recording the proportion of darts that landed inside A. This proportion will be a good simulation-based approximation to the real size (or probability) of the set (or event) A. | ||

===Approach=== | ===Approach=== |

## Revision as of 17:27, 29 January 2008

## Contents |

## General Advance-Placement (AP) Statistics Curriculum - Probability Theory Through Simulation

### Motivation

Many practical examples require probability computations of complex events. Such calculations may be carried out exactly, using the proper probability rules, or approximately using estimation or simulations.

A very simple example is the case of trying to estimate the area of a region, A, embedded in a square of size 1. The area of the region depends on the demarkation of its boundary, as a simple closed curve, as shown on the picture. This problem relates to the problem of computing the probability of the event A as a subset of the sample-space S - square of size 1. In other words, if we were to throw a dart at the square, S, what would be the chance that the dart land inside A (under certain conditions, e.g., the dart must land in S and each location of S is equally likely to be hit by the dart)?

This problem may be solved exactly by using integration, but an easier approximate solution would be throwing 100 darts at the board and recording the proportion of darts that landed inside A. This proportion will be a good simulation-based approximation to the real size (or probability) of the set (or event) A.

### Approach

Models & strategies for solving the problem, data understanding & inference.

- TBD

### Model Validation

Checking/affirming underlying assumptions.

- TBD

### Computational Resources: Internet-based SOCR Tools

- TBD

### Examples

Computer simulations and real observed data.

- TBD

### Hands-on activities

Step-by-step practice problems.

- TBD

### References

- TBD

- SOCR Home page: http://www.socr.ucla.edu

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