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.