Let Z be N (0, 1) with density function and distribution function # (section 3.5). True or false, and explain: (a) The slope of

Let Z be N (0, 1) with density function φ and distribution function #

(section 3.5). True or false, and explain:

(a) The slope of # at x is φ(x).

(b) The area to the left of x under φ is #(x).

(c) P (Z = x) = φ(x).

(d) P (Z < x) = #(x).

(e) P (Z ≤ x) = #(x).

(f) P (x < Z < x + h) .

= φ(x)h if h is small and positive.