PHYSICS 2040
Total 50 marks
Problem Set 1
due September 23
Time is natures way to keep everything from happening all at once.
Grato found in the mens room of the Pecan Street Cafe in Austin, Texas, by John
Archibald Wheeler (the physicist who coined the t
SECTION 2
DISCRETE AND CONTINUOUS RANDOM VARIABLES
1
1. density and cumulative distribution function (cdf)
2. examples of discrete and continuous distributions
3. joint density and joint cdf
4. the empirical cdf
5. random variables, densities and cdf
6. t
D. Joint Distribution and Joint Density
Def. 2.28: a function f(x1, x2) is called a discrete joint density
function if
(1) f(x1, x2) 0 for all real values x1 and x2
(2) cfw_(x1, x2) : f(x1, x2) 0 is finite or at most countably infinite
f(x 1, x 2 ) 1
(3)
C. (Cumulative) Distribution Functions (cdf)
Def. 2.18: A function F: R R is called a (cumulative) distribution
function (c.d.f) if
(i)
F(x) 0 for all x R;
(ii)
F is increasing, that is, if a < b, F(a) F(b)
lim
(iii) x F ( x ) = 1 and x lim F ( x ) = 0
(i
Math 2030-2014 Assignment #4
All page numbers and problems refer to your textbook Pitman. If a problem in the text has more than
one part, hand in only the parts which I ask for. If no parts are stated, then hand in ALL parts. (Example:
3. (a) p. 32 #14 m
PHYSICS 2020
Midterm #1 Equation Sheet
Never memorize something you can look up. Albert Einstein
Constants and Conversion Factors
1 m = 106 m = 109 nm
1 GeV = 103 MeV
e
0
1/40
me (the electron mass)
Mp (the proton mass)
=
=
=
=
=
=
=
Coulombs Law:
F =
The
PHYSICS 2020
Exam Equation Sheet
Never memorize something you can look up. - Albert Einstein
Constants and Conversion Factors
1 m = 106 m = 109 nm
1 GeV = 103 MeV
e
0 = 8.854 pF/m
1/40
0
me (the electron mass)
Mp (the proton mass)
1010 A = 1012 pm = 1015
PHYSICS 2020
Total 42 marks
Solutions to Problem Set 1
was due September 17
He who never made a mistake never made a discovery. Samuel Smiles
1. (8 marks) Consider the vector G = (6,-12,12). What are |G| and G? What angle does
G make with a) the x axis?,
Example 2.52 (Multinomial Distribution)This is the generalization of
the Binomial distribution. Instead of just two possible outcomes (S
or F) we suppose that on each trial there are m possible outcomes
each denoted by 1im. Then the density of the multino