5.5 More on the squareroot law We wish to explore the
reasonableness of the approximation E[1/] 1/. We know from Section 5.8 that, in fact,
E[1/] > 1/.
 Suppose that N is uniformly distributed over the integers
1, 2, . . . , 10. Verify that
 Now suppose that N's distribution is clustered more around
its mean:
Verify in this case that E[1/] 0.466, a result much closer to the desired
approximation.
 Now suppose that E[N] is large and N's
distribution is fairly symmetric about its mean E[N],
which for simplicity we assume to be an integer. Using the squareroot
approximation
(y + )
y^{½} + ½ y^{½}
for  considerably smaller than y >
0, write E[1/] as a series of terms
symmetrically expanded about the mean
