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==
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=== Probability Theory Through Simulation===
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===Motivation===
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Example on how to attach images to Wiki documents in included below (this needs to be replaced by an appropriate figure for this section)!
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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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<center>[[Image:AP_Statistics_Curriculum_2007_IntroVar_Dinov_061407_Fig1.png|500px]]</center>
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[[Image:SOCR_EBook_Dinov_Probability_012908_Fig3.jpg|200px|thumbnail|right]]
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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)?
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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 17:25, 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



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