(a) Show that the standard normal density function (x) is sym- metric about x = 0. That is, show (x) = (x).

(b) Show that (x | ,) is maximized in x at x = . That is, the normal mean is also the mode.

(c) What does the cumulative normal distribution function (x | ,) look like when becomes very large? What does this say about the distribution of samples from this population?

(d) What does look like when is very small? Similarly, what does this suggest about samples from this distribution?