A computer routine called rand (a, b) returns a uniform random number between a and

b. if you want to generate a mean zero, unit variance uniform random number, what values of a and b would you use in the function call?

With a symmetric distribution (uniform is symmetric), mean zero means a=-b where b>0, ex. a=-4, b=4 will give a mean zero.

A uniform random variable with domain (a, b) as given has a variance of

variance = sigma^2 = (1/12) (b-a) ^2.

If we use the domain (a, b), the variance must equal 1.0, or

(1/12) (b-a) ^2 = 1

Solving for (b-a) gives (b-a) = sqrt (12) = 2sqrt (3).

Since a=-b (see first paragraph), (b-a) = 2b=2sqrt (3), or b=sqrt (3).

Hence the values of a and b are (-sqrt (3), sqrt (3), and the function call should be rand (-sqrt (3), sqrt (3)).