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. 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
corrections

4. Normalization of the pdf
When the pdf is ‘normalized’ correctly:
Here,

5. Probability Density & Distribution
Determine Pr[x≤1] using the pdf and using the PDF.
pdf
PDF
Fig. 7.14

6. 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. In-Class Example ∫→ p
C =