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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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Most popular questions from this chapter

Two people are taking turns tossing a pair of coins; the first person to toss two alike wins. What are the probabilities of winning for the first player and for the second player? Hint: Although there are an infinite number of possibilities here (win on first turn, second turn, third turn, etc.), the sum of the probabilities is a geometric serieswhich can be summed; see Chapter 1 if necessary.

By expandingw(x,y,z) in a three-variable power series similarto ,(10.10)show that

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