STAT 390 Homeworks 46 Solutions 9/29 We have that
  2 1 e 2 dx = 1. 2 x
So using the substitution z =
x dx gives dz = , so
2

z  1 e 2 dz = 1. 2
2
Hence 1  z2 e dz = 1,  2 giving the normal density with = 0 , = 1 . 1.34 (d) Let z*
Problem 2.52.
(a) A normal quantile plot of x follows. Clearly the variable, hourly median power, is not normally distributed, as the normal quantile plot is curvilinear.
250 200 150 100 50 0 2 1 0 1 2
power
z quantile
6 5
ln(power)
4 3 2 1
Discrete Mathematical Modeling
Math 381 Course Notes University of Washington
Prof. Sara Billey Fall Quarter, 2008
c R. J. LeVeque
2
Acknowledgments: These notes are based on many quarters of Math 381 at the University of Washington. The original