1. Dene the range of a matrix A.
R(A) = cfw_v | Ax = v for some vector x. In words: The range of A is the set of all vectors v for which the equation Ax = v has a solution. Equivalent denition: Range of A is the span of columns of A. 2. Dene the null spac
Proof that Sample Variance is Unbiased Plus Lots of Other Cool Stuff
Scott D. Anderson http:/www.spelman.edu/~anderson/teaching/437/unbiased/unbiased.html Fall 1999
Expected Value of S2
The following is a proof that the formula for the sample variance, S2
Exponential Distribution
Denition X is said to have an exponential distribution with parameter ( > 0) if the pdf of X is e x x 0 f (x ; ) = 0 otherwise Remark: 1. Usually we use X EXP() to denote that the random variable X has an exponential distribution
POISSON REGRESSION
2
Example applying the Poisson distribution A retrospective occupational follow-up study was conducted among workers of a telecommunications company in the State of New York. The authors wanted to test the null hypothesis that there was
The Poisson Distribution is a discrete distribution. It is often used as a model for the number of events (such as the number of telephone calls at a business or the number of accidents at an intersection) in a specific time period. It is also useful in e
ExponentialDistribution&PoissonProcess
Memorylessness&otherexponentialdistribution properties; PoissonprocessandcompoundP.P.s
1
ExponentialDistribution:BasicFacts
PDF f(t)=
cfw_
e t,t 0
0,t<0
t
CDF Mean Variance
Prcfw_T t)= e udu=1e t(t 0) 0
1 E[T]= 1 Va
Bucknell University
Using ODE45
MATLAB Help
MATLAB's standard solver for ordinary differential equations (ODEs) is the function ode45. This function implements a Runge-Kutta method with a variable time step for efficient computation. ode45 is designed to
68
Theory Supplement Section M
M
PROOF OF THE DIVERGENCE THEOREM AND STOKES THEOREM
In this section we give proofs of the Divergence Theorem and Stokes Theorem using the denitions in Cartesian coordinates.
Proof of the Divergence Theorem
Let F be a smooth