## Tuesday, April 6, 2010

### Statistics Definitions

SAMPLE POINT- each individual outcome of an experiment
SAMPLE SPACE-the collection of all possible sample points in an experiment
EVENT-a collection of sample points
PRIOR PROBABILITY-initial estimate of the probability of an event
RANDOM VARIABLE-a numerical description of the outcome of an experiment
EXPECTED VALUE OF A RANDOM VARIABLE-a measure of the average value of a random variable
VARIANCE OF A RANDOM VARIABLE-a measure of the dispersion of a random variable
PARAMETER-a numerical measure from a population
STATISTIC- a numerical measure from a sample
SAMPLING DISTRIBUTION-a probability distribution for all possible values of a statistic
PROPERTIES OF ESTIMATORS:
Unbiased: Property of a statistic where the expected value of a statistic/estimator = the parameter being estimated
Consistency: as n increases the probability that the value of a statistic/estimator gets closer to the parameter being estimated increases
CENTRAL LIMIT THEOREM-the sampling distribution of the sample mean can be approximated by a normal probability distribution as the sample size becomes large. This holds even if the population from which the sample mean comes from is not normal, or unknown.
ASYMPTOTIC DISTRIBUTION- an estimator’s sampling distribution in large samples
ASYMPTOTIC PROPERTIES OF AN ESTIMATOR- properties of an estimator in large samples