1 / 9

Probability Density Function Concept

Probability Density Function Concept. Consider a signal that varies in time. Figure 7.8. What is the probability that the signal at a future time will reside between x and x + D x?. In-Class Example. Determine the probability that x is between 1 and 7. A consequence of this is that.

arthur-dickson
Download Presentation

Probability Density Function Concept

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. Probability Density Function Concept • Consider a signal that varies in time. Figure 7.8 • What is the probability that the signal at a future time will reside between • x and x + Dx?

  2. In-Class Example • Determine the probability that x is between 1 and 7.

  3. A consequence of this is that corrections PDF pdf Figure 7.14 Probability Distribution Function (PDF) • The probability distribution function (PDF) is related to the integral of the pdf.

  4. When the pdf is ‘normalized’ correctly: Normalization of the pdf Here, >> not normalized So, define pnew(x) = 1/3 p(x) such that

  5. Probability Density & Distribution • Determine Pr[x≤1] using the pdf and using the PDF. pdf PDF Pr[x≤1] = 0.5 / 3.0 = 1/6 = 16.7 % Fig. 7.14

  6. Integrating the pdf expressions give In-Class Example • Determine the expressions for the PDF curve, knowing that of the pdf curve.

  7. In-Class Example N2 molecules travel at speeds in this room according to the Maxwell-Boltzman speed distribution. The probability density function that describes this is: Determine the speed below which 95 % of the molecules travel.

  8. ∫→ 810 m/s In-Class Example p C = pdf PDF

  9. The Normal pdf and PDF Figure 8.4

More Related