Problem Set 4

Due October 4

Problem 1. Consider the distribution function f(x) = C(|x|+1) for -1 < x < 1; otherwise, f(x)=0.

a. Sketch f(x).

b. Determine the normalization constant C.

c. Determine the average value of x.

d. Determine the average value of x².

Problem 2. Consider the distribution function f(x) = C(|x|+1) where x is a discrete variable that can only have the following values: -1/2, 0, 1/2.

a. Sketch a histogram of f(x).

b. Determine the normalization constant C.

c. Determine the average value of x.

d. Determine the average value of x².

Most of these problems require integrals found in the table in Appendix B1.

8-6

8-9

8-41

8-42

8-45. Heat capacity is d<E>/dT. Typo: There should be a "/" before kT in the distribution function.