PH689-01 Fall 2006
Statistical methods for physics and astrophysics
SOLUTIONS to Assignment #1
1. Consider 3 baseball players:
Player A was at bat 200 times, hitting .310;
player B was at bat 250 times, hitting .290;
player C was at bat 300 times, hitting
PH689-01 Fall 2006
Statistical methods for physics and astrophysics
Solutions for Assignment #5
1. Problem 7.2 of Bulmer, part (b).
The score of an IQ test is distributed as a Gaussian of = 100, = 16.
(a) The sampling distribution of the mean with size n=
PH689-01 Fall 2006
Statistical methods for physics and astrophysics
SOLUTIONS to Assignment #4
1. Problem 2.12 from Bevington, Second Edition.
(a) Consider that the number of detected neutrinos in a day follows the Poisson ( = 2):
P (i) =
i
e
i!
P(i >= 8
PH689-01 Fall 2006
Statistical methods for physics and astrophysics
Solutions to Assignment #9
1. Prove that the binomial distribution,
N n N n
pq
n
f (n) =
is the stationary distribution of the basic Ehrenfest chain.
Solution (also provided in class):
Ne
PH689-01 Fall 2006
Statistical methods for physics and astrophysics
SOLUTIONS to Assignment #6
1. Problem 3.2 from Bevington, 2nd edition.
A= D 2
4
Since the function is a power, use (3.28) with a = , b=2
4
A
A
=b
D
D
=2%.
1
Same conclusions if you use th
PH689-01 Fall 2006
Statistical methods for physics and astrophysics
Solutions for Assignment #5
1. Problem 7.2 of Bulmer, part (b).
The score of an IQ test is distributed as a Gaussian of = 100, = 16.
(a) The sampling distribution of the mean with size n=
PH689-01 Fall 2006
Statistical methods for physics and astrophysics
SOLUTIONS to Assignment #4
1. Problem 2.12 from Bevington, Second Edition.
(a) Consider that the number of detected neutrinos in a day follows the Poisson ( = 2):
P (i) =
i
e
i!
P(i >= 8
PH689-01 Fall 2006
Statistical methods for physics and astrophysics
SOLUTIONS to Assignment #3
1. Show that the variance of a binomial distribution equals N p q .
X is a binomial random variable:
E (X 2 ) = N=0
n
= E (X )2 + pqN
N
n
d
n2 pn (1 p)N n = (p
PH689-01 Fall 2006
Statistical methods for physics and astrophysics
SOLUTIONS to assignment #2
1. Find the constant A that makes the following function a probability distribution
function over the interval R:
f (x) = A
1
1+x2
For the same random variable
PH689-01 Fall 2006
Statistical methods for physics and astrophysics
SOLUTIONS to Assignment #6
1. Problem 3.2 from Bevington, 2nd edition.
A= D 2
4
Since the function is a power, use (3.28) with a = , b=2
4
A
A
=b
D
D
=2%.
1
Same conclusions if you use th