Probability and Statistics test 1

Event

A collection of one or more outcomes of an experiment. This includes null as well as S note: An event is said to occur if the outcome of the experiment is one of the members of that event

Continuous Sample Space

A continuous sample space countains an infinite number of points S={x | 0<x<inf}

Discrete Sample Space

A sample space is said to be discrete if it contains either a finite or countably infinite number of points 1. Finite sample space, S={1,2,...,N} 2. Countably infinite sample space, S={1,2,...}

Sample

A subset of the poulation

Population

A well-defined collection of items

Simple Event

An event that contains exactly one outcome of the experiment note: A simple event is sometimes called an elementary event or sample outcome and is denoted by s

Random Experiment

An experiment in which the outcome of the experiment cannot be determined prior to running the experiment

Experiment

Any process that: 1. Has a well defined set of possible outcomes 2. Can be repeated and will result in exactly one of the outcomes

Addition Rule

If A and B are mutually exclusive (disjoint) events, then P(A or B) = P(A) + P(B) If A and B are not mutually exclusive (not disjoint) events, then P(A or B) = P(A) + P(B) - P(A and B)

Experimental Error

Inherent variation among experimental units treated alike

Inferential Statistics

Methods of drawing and measuring reliability of conclusions about a population. The three major branches are: estimation, decision making, and prediction

Descriptive Statistics

Methods of organizing and summarizing data

Treatment

The application of one or more factors

Complement

The complement of an event A is denoted by A' and means that the outcome is NOT in event A

Replication

The experiment must be replicated in order to estimate experimental error. In general the more replicates the better the estimate of experimental error

Randomized Complete Block Design (RCB design)

The experimental units are at random to treatments within each block

Randomization

The experimental units must be randomly divided into groups to avoid unintentional selection bias in constructing the groups

Intersection

The intersection of tow events A and B is denoted by (A n B) or by (A and B) and means that the outcome is in both events A and B

Union

The union of two events is denoted by (A u B) or by (A or B) and means that the outcome is either in event A, or it is in event B, or it is in both events A and B

Independence

Two events A and B are said to be independent if and only if P(A | B) = P(A) or P(B | A) = P(B)

Simple Random Sample

a sampling procedure for which each possible sample of a given size is equally likely to be the one obtained

Designed Experiments

a study where researchers can manipulate the levels of treatment variables. Designed experiments are used to establish cause and effect

Observational Studies

a study where researchers observe characteristics and take measurements. Observational studies reveal associations but they cannot reveal causation

The Multiplication Rule

1. If two events A and B are independent, then P(A and B) = P(A) * P(B) 2. If two events A and B are not independent, then P(A and B) = P(A) * P(B | A) or P(A and B) = P(B) * P(A | B)

Conditional Probability

1. P(A | B) = P(A and B)/P(B) 2. P(B | A) = P(A and B)/P(A)

Completely Random Design (CR design)

Experimental units are assigned to treatments at random

Complementary Events Rule

P(A) = 1 - P(A') or P(A') = 1 - P(A)

Total Probability

P(A) = P(A or B) + P(A and B') or P(A) = P(B) * P(A | B) + P(B') * P(A | B')

Bayes' Rule

P(B | A) = (P(B) * P(A | B))/(P(B) * P(A | B) + P(B') * P(A | B'))

Conditional Probability

P(B | A) = P(A and B)/P(A)

Other Sampling Designs

Systematic Random Sampling, Cluster Sampling, and Stratified Sampling. These sampling methods are described in the text

Experimental Unit

The smallest piece of material to which a treatment is applied. When the experimental unit is a human, the term subject is often used in place of experiment unit

Outcome

The result of performing the experiment

Sample Space

The set of all possible outcomes of an experiment is called the sample space, denoted by S note: One and only one of the outcomes will occur on a given trail of the experiment