New Definitions
What is the definition of a population?
A population refers to the entire group of individuals about which we would like to make a statement.
Everything in the population shares the same:
- Probability distribution
- Statistical models
What is a statistic?
Suppose X_1, X_2, ..., X_n is a (random) sample. A statistic is a function of (X_1, X_2, ..., X_n) that does not depend on any parameters.
A statistic is a random variable.
Parameter definition 1
A parameter is a quantity that index a probability distribution (population) of a random variable.
Parameters include mu, sigma^2,sigma,p .
Moments (expectations) are functions of parameters.
What is a point estimator/estimator?
A point estimator is a statistic that is used to estimate a population parameter.
Examples: Sample mean (barX) is an estimator for population mean (mu)
Parameter definition 2
A parameter is a numerical quantity that describes a population.
Parameters are secrete of nature: UNKNOWN.
What is an estimate?
Estimates are calculated using data, x_1, x_2, ..., x_n. It is the realization (values) of the estimators. Estimates ARE NOT random variables.
What is the definition of a sample?
A sample is a subset of a population. It is a set of random variables that follow the same distribution as the population and is indexed by the same set of parameters.
Denoted by X_1, X_2, ..., X_n
What is the definition of data?
The set of observations of sample is called data. It is the realization (values) of the random variables in the sample. HOWEVER, data IS NOT a set of random variables.
Denoted by x_1, x_2, ..., x_n