Multiple choice. Please answer all parts a-e below. Please show all work and all steps, and mark one answer for each part.

1a.) Let f be the density of the standard normal random variable Z. Let x be an arbitrary real number. What is the relation between f(-x) and f(x)?

a) f(-x)= -f(x)

b) f(-x)=f(x)

c) f(-x)

1b.) Let f be the same as above. What is the absolute maximum of f over the whole real line?

a) 1/sqrt(2pi)

b) 1/((sigma)sqrt(2pi))

c) 1/(sqrt(pi/2))

1c.) This absolute maximum value is attained for x=?

a) 0

b) 2pi

c) pi/2

1d.) Let f be as above. Find the limit of f(x) as x goes to +infinity.

a) 0

b) 1

c) sqrt(2pi

1e.) is the distribution function of the standard normal Z. Find (0).

a) .5

b) pi/2

c) .314