Prob and Stats 3rd

Random Experiment

an experiment that can be repeated numerous times under the same conditions. The results must be independent of one another.

Outcome

the result of a random experiment.

Sample

A smaller group or subset of the population in question

Sample Space

the set of possible outcomes of a random experiment denoted by a capital letter, usually S.

Random Variable

a function that associates a numerical value to every outcome of a random experiment; denoted by a capital letter, usually X.

Discrete random variable

a random variable with a finite number of possible values or an infinite number of values that can be counted.

Continuous random variable

a random variable that can assume an infinite number of values.

Normal (Bell Curve)

a graph that represents the probability density function of a normal probability distribution. It is also called a Gaussian curve named after the mathematician, Carl Friedrich Gauss

Empirical Rule

this rule states that the area of the region between one standard deviation away from the mean is 0.6826 (68.26%) , two standard deviations away from the mean is 0.9544 (95,44%), and three standard deviations away from the mean is 0.9974 (99.74)

Population

a group where members have something in common; that is,the total set of observations that can be made

Sample

a smaller group or subset of the population in question

Parameter

describes an entire population

Statistic

describes only the sample

Simple Random Sampling

The simplest way of getting random sample where each member of the population has an equal chance of being chosen as the sample.

Stratified Random Sampling

This involves selecting a simple random sample from each of a given number of subpopulations proportionally. Each subpopulation is called a stratum (plural: strata).

It is used when the population is heterogeneous. That is, every element of population does not match all the characteristics of the predefined criteria.

Cluster Sampling

The population is first divided into separate groups called clusters. Then, a simple random sample of clusters from the available clusters in the population is selected.

1-in-k Systematic Random Sampling

This involves the random selection of one of the first k elements in an ordered population, and then the systematic selection of every kth element thereafter. In this method, the value of k is first calculated by dividing the population size by the sample size.

Multistage Sampling

Two or more probability techniques are combined. It can be described as sampling within the sample. It is usually used when it is not possible to obtain a representative sample with only one of the aforementioned techniques.