1 / 4

Understanding the Normal Distribution and Numerical Integration Methods

Learn about how Z-values are used to calculate probabilities in the Normal Distribution and why numerical integration methods like Trapezoidal and Simpson's Rule are crucial for solving complex problems efficiently.

dandre
Télécharger la présentation

Understanding the Normal Distribution and Numerical Integration Methods

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Normal Distribution… An important function that can’t be integrated (by elementary methods) and why we need numerical methods!

  2. The Normal Distribution… • Z-values are used to calculate probabilities or estimate the fraction of a statistic that lies within a given range. • For example…. In a Math 205 Midterm exam the average score was 65% and the standard deviation was 10%. Estimate the fraction of the class that scored higher than 85%.

  3. Where do z-values come from? • Easiest way is to numerically integrate

  4. Numerical Integration Methods • Trapezoidal – approximate the function by a series of trapezoids • Simpson’s Method – approximate the function by a series of parabolas! • Error Simpson’s Rule is very robust and an often used numerical scheme

More Related