Homework solutions
Math525
Fall 2003
Text book: Bickel-Doksum, 2nd edition
Assignment # 3
Section 1.4.
1. (a) For any z = 0, 1, 2,
P cfw_Y Z = k|Z = z =
4z
k
4
2
2+z
2k
k = 0, 1, 2
The right hand side gives the hypergeometric distribution H(4 z, 6, 2) (se
Homework solutions
Math525
Fall 2003
Text book: Bickel-Doksum, 2nd edition
Assignment # 1
Section 1.1.
1. (a). Let Xk = the measured diameter of the k-th pebbles (k = 1, 2 ). The
collect data cfw_X1 , , Xn is an i.i.d. and Y = log X1 N (, 2 ) so for each
Homework solutions
Math525
Fall 2003
Text book: Bickel-Doksum, 2nd edition
Assignment # 6
Section 3.4.
1. E X = . So X is unbiased. p(x, ) = x (1 )1x , x = 0, 1.
log p(x, ) = x log + (1 x) log(1 ) and
x 1x
log p(x, ) =
1
2
X
1X 2
log p(X, ) = E
1
2
2
X
X
Homework solutions
Math525
Fall 2003
Text book: Bickel-Doksum, 2nd edition
Assignment # 5
Section 3.2.
2. By the suciency of S
1
B = E[|X] = E[|S] =
(|S)d
0
For any k = 0, 1, n,
(|k) =
1
0
1
n k
(1 )nk
r1 (1 )s1
k+r1 (1 )nk+s1
k
B(r, s)
=
1
n k
B(k + r
Chapter 1: Atoms
Why Study Chemistry?
What is Chemistry?
Chemistry is the study of the properties and
behavior of matter.
Matter is anything that has mass and occupies
space.
How Can Matter Exist?
Solid
Liquid
Gas
How is Matter Classified? Pure Substances
Chapter 3: The QuantumMechanical Model of the Atom
Radiant Energy as Waves
Electromagnetic energy (light) is characterized by
wavelength, frequency, and amplitude.
Electromagnetic Spectrum
Smaller wavelength
Larger/higher frequency
Hearing Colors
Waveleng