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Chapter 15: Q2P (page 765)

Do Problem 6.4 with f(x) in (8.1).

Short Answer

Expert verified

The mean is equal to 0.

The variance is equal to σ2

Step by step solution

01

Given information

A function that is proportional toe-ax2.

02

Definition of variance

A statistical measurement of the dispersion between values in a data collection is known as variance.

03

The density of harmonic oscillator

The probability density functions of a harmonic oscillatorfx=ca.e-ax2.

The density function is gx=12πσ2e-x22σ2

It is the only symmetric function proportional to e-ax2 that integrates to 1.

a=12σ2ca=12πσ2

Hence the mean is equal to 0 and the variance is equal to σ2

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