Solution
= Solution
For $n=100$ and $\tau=1$,
$$
p(0)=1,
\qquad
q(0)=\frac1{1+1/\sqrt{101}}<1.
$$
Both are continuous, so when $|\overline x|$ is sufficiently small,
$$
\boxed{p(\overline x)>q(\overline x)}.
$$
= Solution
For $n=100$ and $\tau=1$,
$$
p(0)=1,
\qquad
q(0)=\frac1{1+1/\sqrt{101}}<1.
$$
Both are continuous, so when $|\overline x|$ is sufficiently small,
$$
\boxed{p(\overline x)>q(\overline x)}.
$$