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