Answers for Assigned Problems

A.

1.1 (a) <j²>=459.571, <j>²=441,
      (b) s=4.309,
      (c) <j²>-<j>²=18.571

1.3 (a) A = Ö(l / p)
      (b) <x> = a, <x²> = a² + 1/(2 l), s = (2l)^-1/2

1.6 Proof.

B   (a) r(q) = 1/p, 0<q< p, and 0 otherwise
      (b) See (a)
      (c) Proof
      (d) <q> = p/2
      (e) r(x) = (1/p)(r² - x²) ^{- 1/2}, for -r <x< r ; 0 otherwise
      (f) <x> = 0, <x²>=r²/2, s = r/Ö2. Note that the easiest way to get these is from part (a).       (g) P=2/p

Last revised 2005/03/04