Probability Density Function Concept

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The Normal Distribution

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Presentation transcript:

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?

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

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

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

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

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

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.

In-Class Example ∫→ p C =