Lecture 10 Notes, Hypothesis Testing
1 Definitions
1.1
Hypothesis Testing
A (parametric) hypothesis is a statement about one or more population
parameters. This hypothesis can be tested using a hypothesis test.
A hypothesis test consists of:
1. Two comple
Lecture 9 Notes, Intervals
1 Interval Estimation
Interval estimation is another approach for estimating a parameter . Interval estimation
consists in finding a random interval that contains the true parameter with probability (1
). Such an interval is ca
Lecture 8 Notes, Estimation
1 Definitions
1.1
Parameter
A pmf/pdf can be equivalently written as fX (x) or fX (x|), where represents the
constants that fully define the distribution. For example, if X is a normally distributed RV,
the constants and will f
Lecture 2 Notes, Discrete and Random Variables
Random Variables
1
1.1
Intuitive Definition
A random variable is a variable with unknown numerical value that can take on, or
represent, any possible element from a sample space. The elements of a sample
spac
Lecture 6 Notes, Normal Distribution
1 Discrete Distributions
1.1
Hypergeometric Distribution
Let the RV X be the total number of successes in a sample of n elements drawn
from a population of N elements with a total number of M successes. Then, the
pmf o
Lecture 7 Notes, Random Sampling
1 Definitions
1.1
Random Sample
Let X1., Xn be mutually independent RVs such that fXi (x) = fXj (x) i = j. Denote fXi (x) = f(x). Then, the collection
X1, ., Xn is called a random sample of size n from the population f(x).
Lecture 5 Notes, Vectors
1 Function of a Random Variable (Univariate Model)
1.1
Discrete Model
Let X be a discrete random variable with pmf fX (x). Define a new random variable Y
as a function of X, Y = r(X). The pmf of Y , fY (y), is derived as follows:
Lecture 1 Notes, Set and Probability
1
Set Theory
1.1
Definitions and Theorems
1. Experiment: any action or process whose outcome is subject to uncertainty.
2. Sample Space: collection of all possible outcomes (or elements) of the
experiment (set S). [Fin
Lecture 4 Notes, Expectations
1 Expected Value
1.1 Univariate Model
Let X be a RV with pmf/pdf f (x). The expected or mean value of X, denoted E(X)
or X , is defined as:
E(X) = X =
xf (x)
(discrete model)
x X
(1)
E(X) = X =
xf (x)dx
(continuous model)
In
Lecture 3 Notes, Multivariable Distribution
1 Multiple Random Variables
1.1
Bivariate Distribution
Many experiments deal with more than one source of uncertainty. For these cases a random
vector must be defined to contain the multiple random variables we