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

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

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

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

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

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

7. In-Class Example N 2 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. In-Class Example ∫→ pdfPDF 810 m/s C = p

9. The Normal pdf and PDF Figure 8.4